Answers
The width of the shade along line AB, using relations in a right triangle, is of:
337.8 mm.
What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is represented by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.The width of the shade along-side line AB is of:
100 mm + e1 + e2.
Considering a bisection at the top corner of the shade, we have that:
e1 is the length opposite side to an angle of 50º in a right triangle with hypotenuse of 150 mm, hence:
sin(50º) = e1/150
e1 = 150 x sin(50º)
e1 = 114.9 mm.
Considering a bisection at the bottom corner of the shade, we have that:
e2 is the length opposite side to an angle of 55º in a right triangle with hypotenuse of 150 mm, hence:
sin(55º) = e2/150
e2 = 150 x sin(55º)
e2 = 122.9 mm.
Hence the total width of the shade is of:
100 mm + e1 + e2 = 100 + 114.9 + 122.9 = 337.8 mm.
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Related Questions
)A math teacher graded 45 problems in of an hour. At that rate, how many problems
can she grade in 1 hour?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
problems
Subnt
Answers
The number of problem that can she grade in hour is 60 problems
The number of problems that math teacher graded in 3/4 of an hour = 45 problem
Here we have to use the unitary method
The unitary method is defined as the method of finding the value of the single unit.
The number of problem that can math teacher grade in 1 hour = The number of problems that math teacher graded in 3/4 of an hour ÷ 3/4
Substitute the value in the equation
The number of problem that can math teacher grade in 1 hour = 45 ÷ (3/4)
= 45 × (4/3)
= 60 problem
Hence, the number of problem that can she grade in hour is 60 problems
The complete question is:
A math teacher graded 45 problems in 3/4 of an hour. At that rate, how many problems can she grade in 1 hour?
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To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)^2 + (4/5)^2 =. The distance between (2, -5) and (-7, -5) is The midpoint of the line segment that joins the given points is given by: (, ).
Answers
(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .
(b) The distance between points (2,-5) and (-7,-5) is 9 units .
(c) The midpoint of the line segment that joins the given points is given by: (-5/2,-5) .
In the question ,
it is given that ,
the points given is (3/5 , 4/5)
(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)^2 + (4/5)^2 = 1
that is
9/25 + 16/25 = 1
25/25 = 1
1 = 1
hence proved that the point (3/5, 4/5) is on the unit circle .
(b) The distance between (2, -5) and (-7, -5) is calculated using the formula
[tex]=[/tex]√(x₂ - x₁)² [tex]+[/tex] (y₂ - y₁)²
= √(-7 - 2)² + (-5 -(-5))²
= √(-9)² + (-5 + 5)²
= √(-9)² = √81
= 9 units
(c) the mid point joining the points (2, -5) and (-7, -5) is (a,b) that is calculated by
a = (2-7)/2 , b = (-5-5)/2
a = -5/2 , b = -10/2
a = -5/2 and b = -5
the mid point is (-5/2,-5) .
Therefore , (a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = 1 .
(b) The distance between points (2, -5) and (-7, -5) is 9 units .
(c) The midpoint of the line segment that joins the given points is given by (-5/2,-5) .
The given question is incomplete , the complete question is
(a) To show that the point (3/5, 4/5) is on the unit circle, we need to prove that (3/5)² + (4/5)² = .
(b) The distance between (2, -5) and (-7, -5) is .
(c) The midpoint of the line segment that joins the given points is given by ( , ) .
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Write an equation the line perpendicular to y-3=-10(x-2) with an x-intercept of (-20, 0) in slope-intercept form.
please show work as detailed as possible
Answers
Answer:
y=1/10x+2
Step-by-step explanation:
y-3=-10(x-2) This equation is in point-slope form so the slope is -10
The perpendicular slope is the negative reciprocal so 1/10.
Slope intercept form is y=mx+b
Plug in the points of the x-intercept and slope into y=mx+b
0=-20(1/10)+b
0=-2+b
b=2
y=1/10x+2
please solve 2y+x=6 and 2y-3x=-2
Answers
Linear Equations
2y+x=6 ... (i)
2y-3x=-2 (ii)
x=2
y=2
To solve this problem, we will use a substitution method.
We would first transform equation (i) to get the formula for x-value.
2y+x=6
x=6-2y... (iii)
Next, we will substitute the equation (iii) into (ii) to find the value of y.
2y-3x=-2
2y-3(6-2y)=-2
2y-18+6y=-2
8y-18=-2
8y=16
y=2... (iv)
Then we would substitute the equation (iii) with the value y on the equation (iv)
x=6-2y
x=6-2(2)
x=6-4
×=2
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Answer:
(2, 2 )
Step-by-step explanation:
2y + x = 6 → (1)
2y - 3x = - 2 → (2)
subtract (2) from (1) term by term to eliminate y
(2y - 2y) + x - (- 3x) = 6 - (- 2) , that is
x + 3x = 6 + 2
4x = 8 ( divide both sides by 4 )
x = 2
substitute x = 2 into either of the 2 equations and solve for y
substituting into (1)
2y + 2 = 6 ( subtract 2 from both sides )
2y = 4 ( divide both sides by 2 )
y = 2
solution is (2, 2 )
Please help me, I don't understand a thing
Answers
Answer:
Step-by-step explanation:
Let M(x,y) be the median of ΔABC through A to BC.M will be the midpoint of BC.x1=5,y1=3x2=3,y2=−1By midpoint formula, x=(x1+x2)/2∴x=(5+3)/2=8/2=4By midpoint formula, y=(y1+y2)/2∴y=(3+(−2))/2=2/2=1Hence the co-ordinates of M are (4,1).By diatnce formula, d(AM)=[(x2−x1)2+(y2−y1)2]x1=7,y1=−3x2=4,y2=1
Hannah's least favorite weekly chore is mowing the lawn, even though it only
takes her about 30 minutes. Her family's lawn is 1,000 square yards, but her
parents are thinking about moving to the country, where they would have 5
acres of land. If the time it takes Hannah to mow a lawn is proportional to its
area, how many hours would it take her to mow 5 acres?
Answers
Answer:
12.1 hours
Step-by-step explanation:
You want to know the mowing time for 5 acres if Hannah can mow 1000 square yards in 1/2 hour.
Unit conversionWe can convert the acreage to square yards to facilitate the calculation:
5 ac × (4840 yd²)/(1 ac) = 24,200 yd²
Mowing rateHannah mows her lawn at the rate of ...
(1000 yd²)/(0.5 h) = 2000 yd²/h
TimeAt this rate, the time it takes for 24200 yd² will be ...
(24,200 yd²)/(2000 yd²/h) = 12.1 h
It would take Hannah 12.1 hours to mow 5 acres.
What is the equation of a circle with center (-3, -5) and radius 4?
O A. (x+3)2 + (y + 5)² = 16
O B. (x-3)2 + (y- 5)² = 4
O C. (x+3)2 + (y + 5)² = 4
O D. (x-3)2+(vy- 5)² = 16
Answers
The equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.
In the given equation we have to find the equation of circle with center and radius.
The given center is (-3, -5).
Radius = 4
The standard equation of a circle with center and radius.
(x−a)^2+(y−b)^2=r^2
where a and b represent a point of center and r represent a radius.
So a=-3, b=-5 and r=4.
Putting the value in the standard equation.
(x−(-3))^2+(y−(-5))^2=(4)^2
Simplifying
(x+3)^2+(y+5)^2=16
Hence, the equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.
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8.26 cats, part i. the following regression output is for predicting the heart weight (in g) of cats from their body weight (in kg). the coefficients are estimated using a dataset of 144 domestic cats
Answers
The correlation coefficient is the square root of the coefficient of determination.
A. The linear model is y' = -0.357+4.034x
Where y' is the predicted heart weight and X is the body weight
B. The intercept of -0.357 is actually showing the non existence of the heart weight when the body weight is absent, ie. When X=0
C. The slope indicates that with each unit increase in the body weight x, the heart weight y increases 4.034 times.
D. R^2 = 64.66% indicates that 64.66% variation in the dependent variable that is explained by our model.
E. Given that the coefficient of determination = 0.6466
Thus the correlation coefficient is the square root of the coefficient of determination
Thus, R = √0.6466 = 0.8041
( Since the slope is positive the correlation ought to be positive)
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The question was incomplete. Check below the complete question.
The following regression output is for predicting the heart weight (in g) of cats from their body weight (in kg). The coefficients are estimated using dataset of 144 domestic cats_ Estimate Std. Error t value Pr(> /tl_ 20 (Intercept _ -0.357 0.692 -0.515 0.607 body wt 4.034 0.250 16.119 0.000 ? 15 1.452 R2 64.66% Radj 64.41% 1 Write out the linear model. [ 10 Interpret the intercept_ Interpret the slope. Interpret R?_ 2.0 Calculate the correlation coefficient 2.5 3.0 3.5 Body weight (kg) 4.0.
Factor completely x^(3)-2x^(2)-24x
Answers
Answer:
x(x - 6)(x + 4)
Step-by-step explanation:
x³ - 2x² - 24x ← factor out x from each term
= x(x² - 2x - 24) ← factor the quadratic
consider the factors of the constant term (- 24) which sum to give the coefficient of the x- term (- 2)
the factors are - 6 and + 4 , then
x² - 2x - 24 = (x - 6)(x + 4)
then
x³ - 2x² - 24x = x(x - 6)(x + 4)
Is 8/20 equal to 4/5
Answers
Answer: no
Step-by-step explanation:
8 and 20 can both be divided by 4
8 divided by 4 = 2
and 20 divided by 4 = 5
based on this, we can tell that 8/20 is not equivalent to 4/ but rather 2/5
I hope that helps
Answer:
No
Step-by-step explanation:
Because if you divide the numerator by something you have to do the same for the denominator. This means the if you do 8÷2 to get 4 then you do 20÷2 you get. 8/20=4/10/2/5
If p + q = 11 and 2p + q = 1 it says that 3p + 2q = 12 but I can't understand how they got to the answer. Please can someone explain? Thank you!
Answers
The value of p and q in the equation are -10 and 21 respectively.
How to solve system of equation?The value of p and q will be found in the equation before we can form another equation with p and q.
Therefore,
p + q = 11
2p+ q = 1
using elimination method
p = 1 - 11
p = -10
q = 11 + 10
q = 21
Therefore,
3p + 2q = 12 (let's check if its correct)
3(-10) + 2(21) = -30 + 42 = 12
Therefore, 3p + 2q = 12 is correct.
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if 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?
Answers
There are 19 triangels can be formed whose vertices are among the 9 points.
A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides. In other words, a triangle is defined as a three-sided two-dimensional figure whose interior angles are equal to 180°.
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.
From the question, we know that we have 9 point from 2 line parallel. There are 19 triangels (the same shape is not counted twice) can be formed whose vertices are among the 9 points that shown in the following picture.
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suppose you plot the location of the animals on a number line which animale would represent by the point farthest from 0 on the number line ? explaine
Answers
The animal that is farthest from 0 on the number line is the Fanfin anglerfish.
What number is farthest from 0 on the number line?
A number line is a marked straight line that is used to visually represent real numbers.
The values given in the table are negative number. A negative number is a number that has a value less than zero. A negative number is represented with a minus sign. The table has decimals, mixed numbers and fractions.
The larger a number is, the farther the distance of the number from 0 on the number line. In the given table, the largest number is -2 1/4. Thus, -2 1/4 is the farthest from the number line.
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Ann and Ben translate documents from German to English.
A set of documents that would take Ann 10 days would take Ben 12 days.
Ann starts to translate the document.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
Answers
They would require more 4 8/22 days to complete the work.
Ann can translate the document in 10days
In 1 day he can translate 1/10 of the document
In 2 days he translates = 2 x 1/10
Ben can translate the same document in 12 days
In 1 day he can translate 1/12
Work left after Ann works for 2 days is 1 - 2/10 = 8/10
When working together they can work in 1 day is= 1/10 + 1/12 = 22/120
They do 22/120 work in 1 day
For 1 work, they require 1/(22/120) = 120/22
for 8/10, they would require (120/22)(8/10) = 96/22 = 4 8/22
Therefore, They would require more 4 8/22 days to complete the work.
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the radius of a circle is 15inches. what is the circumference of the circle? writte your answer using pie.
Answers
Answer:
circumference of the circle is= 2πr
if radius is 15 then we should put that into the formula
30π
if pie is given as 3.14 then it would be
94.2
good luck
Answer:
30 pi inches
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi * r
C = 2 * pi * 15
C = 30 pi inches
PLEASE HELP- I cant figure out this problem
Answers
Step by step
|-2x|=4
the absolute sign means we have to solve for both positive and negative
-2x = 4 and - -2x = 4
-2x = 4
-2/-2 x = 4/-2
x = -2
- -2x = 4 (two negatives makes a positive)
2x =4
2/2 x = 4/2
x = 2
t
f(t) = t - 8
h(t) = −2t
f(h(-5)) =
Answers
⇒Let us first find the expression of f(h(t))
⇒It means in the expression of f in the place of t you will plug in the value of what h is equal to.
[tex]f(h(t))=(-2t)-8\\f(h(t))=-2t-8[/tex]
Now f(h(-5)) means in the place of t you will plug in -5 and simplify.
[tex]f(h(-5))=-2(-5)-8\\\\f(h(-5))=10-8\\f(h(-5))=2[/tex]
An object is dropped from a height of 1, 600 feet. The amount of time, in seconds, the object takes to hit the ground can be
Found by solving the equation -16r2+1, 600 = 0. How many seconds will it take to hit the ground?
10?,50?,10 or -10?,100?
Answers
The time taken by the object to hit the ground is 10 seconds , the correct option is (a) .
In the question ,
it is given that ,
the object is dropped from the height of 1600 feet ,
So , the height h(t) = 1600
the equation representing the height of the object at time t is ,
h(t) = 16t² + 155
Substituting the height h(t) = 1600
16t² + 155 = 1600
16t² = 1600 - 155
16t² = 1445
t² = 1445/16
t² = 90.31
t = √90.31
t = 9.503
t ≈ 10 seconds
Therefore , The time taken by the object to hit the ground is 10 seconds .
The given question is incomplete , the compete question is
An object is dropped from a height of 1,600 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation 16t² + 155 = h(t) . How many seconds will it take to hit the ground ?
(a) 10
(b) 50
(c) 100
(d) 500
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Alexander buys ice cream and oranges at the store.
• He pays a total of $34.07.
• He pays $5.65 for the ice cream.
• He buys 7 bags of oranges that each cost the same amount.
Which tape diagram could be used to represent the context if x
represents how much each bag of oranges costs?
Answers
If x represents the cost of each bag of oranges then the equation will be 7x+5.65 = 34.07 and the value of x is $4.06.
According to the question,
We have the following information:
Alexander buys ice cream and oranges at the store.
• He pays a total of $34.07.
• He pays $5.65 for the ice cream.
• He buys 7 bags of oranges that each cost the same amount.
Let's take the cost of each bag of oranges to be $x.
We have the following equation:
7x+5.65 = 34.07
Subtracting 5.65 from both sides:
7x = 34.07-5.65
7x = 28.42
x = 28.42/7
x = 4.06
Hence, if x represents the cost of each bag of oranges then the equation will be 7x+5.65 = 34.07 and the value of x is $4.06.
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What is the equation of the function
Answers
The equation of line will be given as y = 3x + 24
Given,
The graph of a linear function passes through the points (4, 24) and (6, 30).
The equation of the line will be given as:-
y - y₁ = m ( x - x₁)
Slope m will be calculated as:-
m = (y₂ - y₁) / (x₂ - x₁) = (30 - 24) / (6 - 4) = 6/2 = 3
The equation will be:-
y - 24 = 3 ( x - 4 )
y = 3x - 12 + 24
y = 3x + 24
Therefore the equation of the line will be given as y = 3x + 24.
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Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. the ordered pair (2, - 2) y = -x - 2.
Answers
The equation of the parallel line is y = -x
How to determine the line equation?The equation is given as
y = -x - 2
The point is also given as
point = (2, -2)
The equation of a line can be represented as
y = mx + c
Where
slope = m
By comparing the equations, we have:
m = -1
This means that the slope of y = -x - 2 is -1
The slopes of parallel lines are equal
This means that the slope of the other line is -1
The equation of the parallel line is then calculated as
y = m(x - x₁) +y₁
Where
m = -1
(x₁, y₁) = (2, -2)
So, we have
y = -1(x - 2) - 2
Open the brackets and evaluate
y = -x
Hence, the parallel line has an equation of y = -x
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9. [-10, ∞)
Interval notation
Answers
The inequality of the interval notation [-10, ∞) is x ≥ -10
The given interval notation is
[-10, ∞)
We have to convert the interval notation to inequality
The inequality is the mathematical statement that shows the relationship between two expression with inequality sign. The inequality signs are less than, less than or equal, greater than, greater than or equal. The inequality consist of different variables, numbers and mathematical operators.
Interval notation is defined as the method of writing subsets of the real number line
The given interval notation is
[-10, ∞)
Convert the interval notation to inequality
x ≥ -10
Hence, the inequality of the interval notation [-10, ∞) is x ≥ -10
The complete question is
Convert the interval notation [-10, ∞) to inequality
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2 lines 3y-2x=21 and 4y+5x=5, intersect at the point Q. Find the coordinates of Q
Answers
Answer: (-3,5)
Step-by-Step Solution:
1. Set 1 equation equal to y
3y-2x=21
3y=2x+21
y=2/3x+7
2. Set the other equation equal to y
4y+5x=5
4y=-5x+5
y=-5/4x+5/4
3. Set the equations equal to each other, and solve for x
2/3x+7=-5/4x+5/4
2/3x+23/4=-5/4x
(Multiply by 12 on both sides to get rid of fractions)
8x+69=-15x
8x=-15x-69
23x=-69
x=-3
4. Solve for y
(Choose any of the equations)
y=2/3x+7
y=2/3(-3)+7
y=-2+7
y=5
ANSWER: (-3,5)
Show all work to multiply (3+√16) (6-√64)
Answers
After the multiplication of (3+√16) (6-√64), the resultant answer is -14.
What is multiplication?Multiplying in math is the same as adding equal groups.
The number of items in the group grows as we multiply.
Parts of a multiplication issue include the product, the two factors, and the product.
The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.
So, the multiplication of:
(3+√16) (6-√64)
Now, multiply as follows:
(3+√16) (6-√64)
We know that: 3+√16 = 7
7(6-√64)
We know that: 6-√64 = -2
7(-2)
-14
Therefore, after the multiplication of (3+√16) (6-√64), the resultant answer is -14.
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John uses 4 cups of flour for every 4/7 cups of chocolate chips. How much flour will he use for one cup of chocolate chips?
Answers
Answer:
7
Step-by-step explanation:
4 divided by 4/7 = 7
A vehicle purchased for $27500 depreciates at a constant rate of 8% Determine the approximate value of the vehicle 10 years after purchase Round to the nearest whole number.
Answers
The approximate value of the vehicle 10 years after purchase is $11,945.68.
What is the approximate value of the vehicle?Depreciation is when the value of an asset falls with the passage of time as a result of wear and tear of the asset. Deprecation would reduce the price of the vehicle each year.
The equation that can be used to determine the value of the vehicle after 10 years is:
FV = P (1 - r)^t
Where:
FV= value of the vehicle in 10 years P = value of the vehicle when it was purchased r = rate of decline t = number of yearsFV = 27,500 (1 - 0.08)^10
FV = 27,500 x (0.92^10)
FV = $11,945.68
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What is the argument of (1+i)^4
Answers
The fourth power of the complex number 1 + i has an argument of π radians.
How to determine the argument of the power of a complex number
In this problem we find a complex number of the form z = (a + i b)ⁿ, where n is the grade of the power of the complex number, whose expanded form is obtained by the De Moivre's theorem:
(a + i b)ⁿ = rⁿ · (cos nθ + i sin nθ)
Where:
r - Norm of the complex number.θ - Argument of the complex number, in radians.And the norm and the argument of the complex number are, respectively:
Norm
r = √(a² + b²)
Argument
θ = tan⁻¹ (b / a)
First, determine the components of the complex number and its power:
a = b = 1; n = 4
Second, calculate the argument of the complex number:
θ = tan⁻¹ 1
θ = π / 4 rad.
Third, find the argument of the power of the complex number according to De Moivre's theorem:
θ' = 4 · (π / 4)
θ' = π
The argument of the power of the complex number is π radians.
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Si los lados de un cuadrado miden 3 cm cuántos centímetros cuadrados medirá su área.
Answers
The area of the square that has 3 cm of side is 9 cm^2
The formula and procedure to solve this geometry exercise is:
A = s²
Where:
A = area of the squares = sideProblem information:
A = ?s = 3 cmUsing the formula of the square area we get:
A = s²
A = (3 cm)²
A = 9 cm²
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft2, m2
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A boat is heading towards a lighthouse, where Deion is watching from a vertical distance of 140 feet above the water. Deion measures an angle of depression to the boat at point AA to be 15^{\circ}
∘
. At some later time, Deion takes another measurement and finds the angle of depression to the boat (now at point BB) to be 51^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Answers
Using trigonometric ratio, the horizontal distance from A to B is 314 feet
Trigonometric RatioTrigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.
To calculate the distance from point A to point B, we can use trigonometric ratio here.
Note: We are going to add the two angles and then use the vertical distance as the adjacent side of the triangle.
Data;
Angle = 66°Adjacent = 140ftOpposite = ABUsing tangent of the angle;
Tanθ = opposite / adjacent
tan 66 = AB / 140
AB = 140 tan66
AB = 314ft
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1) Sarah received three fifths of her sister's book collection. If Sarah received 18
books, how many books did her sister have before giving any to Sarah?
Answers
The number of books that her sister has before giving any to Sarah is 30 books
Sarah received three fifths of her sister's book collection
Number of books that Sarah received = 18 books
The fraction of the books that Sarah received = 3/5
Consider the total number of books as x
Then we have to find the total number of books
So the equation will be
x × (3/5) = 18
Divide the terms in the equation
x × 0.6 = 18
Move 0.6 to the right hand side of the equation
x = 18 / 0.6
Divide the terms
x = 30 books
Hence, number of books that her sister has before giving any to Sarah is 30 books
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