a ranger is at the top of a 200 foot tall lookout tower. she spots a fire at an angle of depression of 3° from the top of her tower. To the nearest tenth of a foot, how far away is the fire?
Answers
Step-by-step explanation:
tan3 = 200/x
x = 200/tan3
The question is incomplete. The right question is:
A ranger spots a fire while on a 200-foot observation tower. The angle of depression from the tower to the fire is 3°. To the nearest tenth of a foot, how far away is the fire from the base of the tower?
The distance between the fire and the base of the tower is 3816.2 feet.
What is the concept of height and distances?Heights and Distances is a trigonometric application-based concept, where we try to form a right-angled triangle of the given conditions, take the angles of elevation and depression and try to find the unknowns.
How do we solve the given question?We are given that a ranger spots a fire while on a 200-foot observation tower. The angle of depression from the tower to the fire is 3°.
We are asked to find the distance between the fire and the base of the tower.
We let the 200-foot observation tower be AB. Let the point of fire be C. Join BC and AC to complete the right-angled triangle ABC, with ∠B = 90°. The ranger from the top of the tower has a 3° angle of depression to the fire. We draw the horizontal line of sight AD. Now the angle of depression can be shown by the ∠DAC = 3°.
We let the distance between the fire and the foot of the tower be x foot.
∠BCA = ∠DAC = 3° (alternate angles).
Also, ∠BAC = 180° - 90° - 3° = 87° (using angle sum property of triangles)
In ΔABC,
tan ∠BAC = BC/AB (tan θ = perpendicular/base)
or, tan 87° = x/200
or, x = 200*tan87° = 200*19.0811 = 3816.22 = 3816.2 (rounding to nearest tenth).
∴ The distance between the fire and the base of the tower is 3816.2 feet.
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Related Questions
simplify the ratio 25:15:10
Answers
Answer:
60%
Convert fraction (ratio) 15 / 25 Answer: 60%
Unit 7: Polygons & Quadrilaterals
Homework 3: Rectangles
a 2-page document! **
Answers
Answer:
VW = 31
WX = 19
YW = [tex]\sqrt{1322}[/tex]
ZX = ([tex]\sqrt{1322}[/tex]) / 2
VX = [tex]\sqrt{1322}[/tex]
Step-by-step explanation:
[tex]YW^{2}[/tex] = [tex]19^{2}[/tex] + [tex]31^{2}[/tex]
[tex]19^{2}[/tex] + [tex]31^{2}[/tex] = 1322
ZX = YW/2 = VX/2
Measures of the different sides of the rectangle will be,
YX = 31 units
WX = 19 units
VW = 36.36 units
ZX = 18.18 units
VX = 36.36 units
Quadrilateral VWXY is a rectangle.
Properties of a rectangle,
Opposite sides of a rectangle are equal.Diagonals of a rectangle bisect each other.Diagonals are equal in measure.YX = VW = 31 units
VY = WX = 19 units
By applying Pythagoras Theorem in right triangle ΔWXY,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
(WY)² = (WX)² + (XY)²
YW = [tex]\sqrt{19^2+31^2}[/tex]
= [tex]\sqrt{1322}[/tex]
= 36.36 units
ZX = [tex]\frac{1}{2}(YW)[/tex]
= [tex]\frac{1}{2}(36.36)[/tex]
= 18.18 units
VX = YW = 36.36 units
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Can someone please help me with this it’s really important
Answers
Answer: i would say 30 + 20 - 10 - 20 - 0
sorry if i am wrong
Step-by-step explanation:
The cafeteria bought 200 French bread pizzas for lunch next week. If they had bought the pizza last week while it was on sale, it would only have cost $ 2.00 per pizza. Now, 7 days later, the price is $ 3.78 per pizza. How much money could they have saved if they bought the pizza last week?
Answers
Answer:
$356
Step-by-step explanation:
To solve this problem, use this: (200 * 3.78) - (200 * 2)
(200 * 3.78) - (200 * 2)
200 * 3.78 is the same as 2 * 378, which is 756.
756 - (200 * 2)
200 * 2 is the same as 4 * 100, which is 400.
756 - 400
Subtract 400 from 756 to get 356.
356
If they brought the pizza last week, the school could have saved $356.
plz help this is due tomorrow
[tex](4 + \sqrt{2} )(6 - \sqrt{2} )[/tex]
Answers
Answer:
22 + 2|/2
Step-by-step explanation:
24 - 4|/2 + 6|/2 - |/4
24 + 2|/2 - 2
24 - 2 + 2|/2
22 + 2|/2
note: |/ means root
couldn't find a sign for root so just makeshift with that
hope it helps.
hii please help i’ll give brainliest
Answers
Answer: -(-3)
Step-by-step explanation:
a double negative would equal to a positive :)
hey ma i need your help on this plz and ill give you a branist or wtv its called
Answers
Hi there!
[tex]\large\boxed{\text{ sum = 180(n - 2)}}[/tex]
This is the formula for finding the sum of interior angles for a polygon with a number of sides "n".
We can also prove this from the table:
Triangle ⇒ 3 sides: 180(3 - 2) = 180°
Quadrilateral ⇒ 4 sides: 180(4 - 2) = 360°
Pentagon ⇒ 5 sides: 180(5 - 2) = 540°
...And so forth. We can write this as for any polygon with "n" sides:
180(n - 2) = sum (°)
Can someone help find the center and the equation
Answers
Answer: (x + 4)^2 + (y - 3)^2 = 50
Step-by-step explanation:
Given: x^2 + y^2 + 8x - 6y - 25 =0, which the general form of the circle.
Solution:
Complete the square formula: (x - h)^2 + (y - k)^2 = r^2
Group similar term together on the left side of the equation and move the constant to right side of the equation ( remember to change the sign of the constant.
x^2 + y^2 + 8x - 6y - 25 =0
x^2 + 8x + y^2 - 6y = 25
Complete the Square: (x^2 + 8x + _____) + (y^2 - 6y + _____) = 25
Take half of the coefficient of the linear term for each variable, square the quotient, and add the answer to both side of the equation.
half of the coefficient of the linear term: ( 8/2)^2 = 16 and (-6/2)^2 = 9
(x^2 + 8x + 16) + (y^2 - 6y + 9) = 25 + 16 + 9
Each quality is a trinomial square and need to be factored
(x + 4)^2 + (y - 3)^2 = 50
Help me with this math problem please:):)
Answers
Malala is following this recipe for bread rolls.
She uses 400 g of flour.
How much of the other ingredients does she use?
Recipe: Makes 12 bread rolls
600 g flour
12 g salt
9 g yeast
42 mL oil
330 mL water
Answers
400
10
7
40
130
(not sure if this helped but yeah)
A man drove 450 mi. at an average rate of 45 mi./hr. How long did it take him?
Answers
Answer:
10 hours
Step-by-step explanation:
450 ÷ 45 = 10 hours
plss help if u do u get brainlist and help asap school bitterly almost done
Answers
Answer:
w+8²
p+30÷p²
4(9+y)
Step-by-step explanation:
Answer:
Answers are below.
Step-by-step explanation:
1. [tex]C^{3}[/tex]
2. A + C / 3
Second exercise:
1. w + (8 x 2)
2. 30 + p / p
3. 4 (9 + y)
hope this helps and is right :) p.s. i really need brainliest.
if my answers are wrong, then i am incredibly sorry!
An alligator farm has two baby alligators. Alligator A is 6 inches long and is growing at a rate
of 0.6 inches per month. Alligator B is 4 inches long and has a growth rate of 0.8 inches per
month. Let m represent the number of months and L represent the length of the alligator.
At what month are both alligators the same length?
a. 12 months
b. 14 months
c. 10 months
Answers
Answer:
10 months
Step-by-step explanation:
.8x+4=.6x+6
.8x=.6x+2
.2x=2
x=10
what is the area and yard of 15 and 4
Answers
Answer:
The area and yard is 60.
Step-by-step explanation:
15 x 4 = 60
Let me know if that helps!
The vertex of this parabola is at (-5, 4). Which of the following could be its
equation?
(-5, 4)
A. y* -(x + 5)2 - 4
B. y = -(x - 5)2 - 4
C. y = -(x - 5)2 + 4
D. y = -(x + 5)2 + 4
Answers
Answer:
D
Step-by-step explanation:
Because the x-coordinate of the vertex is negative, only A or D could be the correct equation for this parabola. D is correct because its constant (4) matches the y-coordinate of the vertex (-5, 4).
Answer:
y = -(x + 5)2 + 4
Step-by-step explanation:
In a bag there are 3 red marbles, 2 yellow marbles and 1 blue marble. After a marble is selected, it is replaced. After 40 attempts at drawing two marbles from the bag, there were three instances where a blue marble then a yellow marble was pulled. What is the percent difference between the theoretical probability and the experimental probability?
75%
26%
56%
35%
Answers
Answer:
35%
Step-by-step explanation:
The percent error can be found using the
|Experimental value - Theoretical value| divided by |Theoretical value| and multiplied by 100.
I hope this helps
Here, the experimental probability is 1/4 and theoretical probability is 1/18.Then the percent difference between the theoretical probability and the experimental probability is 56%.
What is probability ?The probability is a measure of chances that an event to take place.
Given that,
red marbles = 3
blue marbles =1
yellow marbles = 2
Then.
theoretical probability of selecting a blue marble followed by a yellow marble is:
P(blue and yellow) = P(blue) x P(yellow) = (1/6) x (2/6) = 1/18
Since the marbles are replaced after each draw, the probability of this event is the same for every draw.
The experimental probability of selecting a blue marble followed by a yellow marble after 40 attempts is:
(3/6) x (2/6) x (40 attempts) = 10
Therefore, the experimental probability is 10/40 = 1/4
The percent difference between the theoretical probability and the experimental probability is:
| (experimental probability - theoretical probability) / theoretical probability | x 100%
= | (1/4 - 1/18) / (1/18) | x 100%
= 0.583 x 100%
= 58.3%
Therefore, the percent difference between the theoretical probability and the experimental probability is approximately 58.3%, which is closest to the option 56%.
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Maths equation please help
Answers
Answer:
V=120cm³
Step-by-step explanation:
v=12(5)(6)-4(10)(6)
v=120cm³
hope it helps...
have a great day!!
PLEASE HELP I WILL GIVE BRAINIEST. What is the Median?
Answers
Answer:
DA MIDDLE LINE. 6
If f(x) = 3^(x + 4), find f(2).
Answers
Answer:
18
Step-by-step explanation:
What is the name of segment BD ?!
Answers
Answer:
diameter
Step-by-step explanation:
BD is the diameter of the circle.
Consider the quadratic function y = 1/5(x - 2)2 + 5.
Which statements are true about the function and its graph? Select two options.
The vertex of the function is (-2,5).
There are no real roots for the function.
The graph of the function opens down.
The graph contains the point (2,5).
The graph intersects the x-axis at one unique point.
Answers
Answer:
Step-by-step explanation:
There are no real roots and the graph contains point (2,5). Notice it is in vertex form. So there must be a point at x = 2 and y = 5. However, if it is the vertex and it opens upwards, that means it cannot intersect the x axis. So 2 and 4 are the correct answers I believe.
if someone can do this? thanks<3
Answers
Answer:
x=16y=76r=494n=108m=45t=793b=81z=352x=33p=564y=109k=126Step-by-step explanation:
I used a calculator. :)
The math problem is in picture
Answers
Answer:
B
Step-by-step explanation:
Welcome for the answer!Answer:
my best guess would be B
Step-by-step explanation:
3.61 + 1.23 = 4.48
2X
[tex]2x + 4 = 0[/tex]
Answers
Answer:
The value of x = -2
Step-by-step explanation:
Given equation:
2x + 4 = 0
Find:
The value of x
Computation:
We know that given equation 2x + 4 = 0 is a liner equation with only one variable.
So, we can solve this by elimination method
2x + 4 = 0
Step 1 :
Subtract 4 from both side
2x + 4 - 4 = 0 - 4
2x = -4
Divide 2 from both side
2x / 2 = -4 / 2
x = -2
The value of x = -2
Megan has a baseball card collection containing 10 cards. She graph the value of these 10 cards on a scatterplot as shown
Answers
Answer:
a basketball card generally increases in value over time (second one)
Step-by-step explanation:
1. it doesn't always increase
3.No it would be around 0.75
4.No it would be around $5.50 I think
Select the correct answer.
Consider this equation.
sin()
4729
29
If 8 is an angle in quadrant IV, what is the value of cos();
OA.
OB.
4729
29
V377
29
4729
29
OC.
OD
V377
29
Answers
Answer:
377/29
Step-by-step explanation:
this is the answer for plato, i took the test btw
For the given value of sin, the value of cosΘ will be 0.73.
What is trigonometry?A right-angle triangle's sides, angles, and relationship to each other are the subject of the mathematical discipline of trigonometry. The pair ratio of a right-angled triangle is known as the trigonometric ratio.
It is given that, sinΘ= -4√29 / 29
Θ=sin⁻¹(-4√29 / 29)
Θ= -0.74
The value of cosΘ is obtained as,
=cosΘ
=cos( -0.74)
=0.73
Thus, the value of cosΘ will be 0.73.
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What are the coordinates of the point (-1, 5) when it is reflected across the y-axis? *
Answers
Answer:
1,5
Step-by-step explanation:
when reflecting across y-axis it'll be in the same order, but using whatever form that quarter of the coordinate plane is in (e.g. 5,7 ----> -5,7)
PLEASE HKEP I AM BEGGING YOU ASAPPP I WILL GIVE I PRONIS I WILL GIVE EXTRA POINTS AND BRAINLIEST!!!!!!!
Answers
D(2)
C(6)
A(5)
B(4)
https://www.mathsisfun.com/definitions/coefficient.html
Answer:
1 eafbcd 2 12
St 3 \ep-by-step explanation:
Gabriele's Pie Shop sold 80 pies last month: 7/10 were apple pies and 1/10 were peach pies. How many pies were neither apple nor peach?
a.)40
b.)32
c.)16
d.)9
Answers
Answer:
16 pies were neither apple nor peach.
Step-by-step explanation:
8/10, or 4/5 of the 80 apple pies were either apple or peach, which 4/5 of 80 is 64. The remaining pies will be neither apple nor peach. 80 - 64 = 16.
Can someone help me
Answers
Answer:
26.6666667
Step-by-step explanation: