The laws of cosines and law of sines can be used given that two sides
and an included angle, or two angles a side are known.
Response:
1. The other angles in the triangle formed by the buoy are approximately;
31.1° and 40.9°2. Distance of the helicopter from the first island is approximately;
14.5 milesHow is the Law of Sines and Cosines used?Given parameters are;
Distance of the buoy from the easternmost point of a boat = 19 yards
Distance of the buoy from the westernmost point of the other boat = 15 yards
Angle formed from the buoy to the two boats = 108°
Distance between the two boats, d, is given by the law of cosines, as follows;
d² = 19² + 15² - 2 × 19 × 15 × cos(108°) = 586 - 570·cos(108°)
d = √(586 - 570·cos(108°))
By the law of Sines, we have;
[tex]\dfrac{d}{sin(108^{\circ})} = \mathbf{\dfrac{15}{sin(Angle \ formed \ from \ the \ boat \ on \ the \ West, \ \theta_1)}}[/tex]
Which gives;
[tex]sin(\theta_1) = \mathbf{ \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} }}[/tex]
The o
[tex]\theta_1 = arcsin \left( \dfrac{15 \times sin(108^{\circ})}{\sqrt{586 - 570 \cdot cos(108^{\circ})} } \right) \approx \mathbf{31.1^{\circ}}[/tex]
The other angles formed in the triangle containing the buoy are;
θ₁ ≈ 31.1θ₂ ≈ 180° - 108° - 31.1° ≈ 40.9°2. Distance between the two islands = 20 miles
Angle of elevation with one island = 15°
Angle of elevation with the second island = 35°
Required:
The mileage (distance travelled) of the helicopter.
Solution:
Let A represent the island that has an angle of elevation to the helicopter
of 15°, and let B represent the other island.
Angle formed by the helicopter and the two island, θ, is found as follows;
θ = 180° - (15° + 35°) = 130°
By the Law of Sines, we have;
[tex]\dfrac{20}{sin(130^{\circ})} = \mathbf{ \dfrac{Distance \ from \ island \ A }{sin(35^{\circ})}}[/tex]
Which gives;
[tex]Distance \ of \ helicopter \ from \ island \ A = \mathbf{ \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ})}[/tex]
[tex]Mileage \ from \ island \ A = \dfrac{20}{sin(130^{\circ})} \times sin(35^{\circ}) \times cos(15^{\circ}) \approx 14.5[/tex]
The mileage of the helicopter from the first island is approximately 14.5 milesLearn more about the Law of Sines and Cosines here:
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Can you give me the answer to this? I would appreciate it!
Thx
Answer:
7,912.8 inch³ of aluminum is needed to make 70 metal balls
Step-by-step explanation:
r = 3 inches and π = 3.14
single aluminum ball, 113.04 inch³ of aluminum
113.04 inch³ of aluminum is used for 1 ball, then we multiply 70 with this value to determine the aluminum needed for 70 such balls.
Pls solve this I can do it after school I can do it after school , I’m going to cry again
Answer:
s = 71
j = 23
71 = 3j+2
71 - 2 = 3j
39 = 3j
j = 23
Answer:
j=23
s=71
Step-by-step explanation:
Here we have two parallel lines lines( UB and DK).
And we have another line, called a transversal that intersects( crosses) both parallel line. Doing so creates the following angles,
Vertical Angles, Angles are equal in measure Alternate Exterior Angles, Angles are equalAlternate Interior Angles. Angles are equalConsective Angles. Angles are equalLinear Pair Angles. Angles add up to 180So now we look at the graph
First, we know that 3j+2 and s are vertical angles since they are across of each other. So they are equal to each other so let look at another angle first.
3j+s and 71 are Alternate Interior Angles since they lie inside the transversal and are across from each other.
Since they are Alternate Interior Angles, they are equal.
So we set them equal to each other.
[tex]3j + 2 = 71[/tex]
Subtract 2 from both sides
[tex]3j = 69[/tex]
Divide both sides by 3
[tex]j = 23[/tex]
The value of j is 23.
Know to find S, we know s is equal to 3j+2, which when we plug in 23 for j, we get 71.
So s=71
Angle STV is a straight angle. The measure of WTV angle is 40. The measure of STW angle is x . What is the value of x?
Answer: 140
Step-by-step explanation:
We know that the angle measures must add to 180 deg, so:
40 + x = 180
x = 140.
I need help factoring an equation.
Answer:
30n^15
multiply exponents add reg numbers
19. A bird flies at 12 miles/hour. How long does he take to fly 36 miles?
Answer:
He flew for 3 hours
Step-by-step explanation:
in this question we can use the formula :
[tex] \boxed{t = \frac{s}{v}} [/tex]
t is time
s is distance
v is Speed
_________________
We know that :
v = 12 miles/hour
s = 36 miles
So :
[tex] t = \frac{s}{v} = \frac{36}{12} [/tex]
[tex] \boxed{t = 3 \: hours}[/tex]
______________________
Find the volume of this cylinder if it has a diameter of 4mm and a height of
14mm.
Answer:
V≈1.76×10-7m³
Step-by-step explanation:
PLEASE HELP HURRY WILL MARK THE BRAINLIEST ONLY ANSWER IF U KNOW 25 POINTS!!!what is the value expression 2⁴ plus 3²
Answer:
25
Step-by-step explanation:
2x2x2x2=16
3x3=9
16 + 9= 25
Find the value of x.
The sum of triangle angles = 180
180 = 90 + 2x +15 + x
75 = 3x
x = 25
Answer:
→x=25°
Step-by-step explanation:
→2x+15+x+90°=180°[Sum of a triangle is 180]
→3x+105°=180°
→3x=180°-105°
→x=75°/3
→x=25°
Hope it will help you.
Find the length y of the minute hand in 3 sf
Please help
Answer:
135 cm
Step-by-step explanation:
[tex] \cos(43) = \frac{75}{y} [/tex]
[tex]y = \frac{75}{ \cos(43) } [/tex]
[tex]y = 135[/tex]
Answer:
y ≈ 102 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos43° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{75}{y}[/tex] ( multiply both sides by y )
y × cos43° = 75 ( divide both sides by cos43° )
y = [tex]\frac{75}{cos43}[/tex] ≈ 102 cm ( to 3 sf )
helpp! im 2 lazy to do it
Answer:
28. add them all together
Answer:
the answer is 28
Step-by-step explanation:
you have good taste in music
Suppose you have a $4-off coupon at a fabric store. You buy fabric that costs $6.75 per yard. Write an equation that models the total amount of money y you pay if you buy x yards of fabric
Answer: 6.75x - 4
Step-by-step explanation:
6.75x - 4
please help i am having a bad day this is my last question
can you tell me the answer please
Answer:
11
Step-by-step explanation:
140-129=11
Answer:
140 - 129
Step-by-step explanation:
If Alyanna has more cookies than Alyssa, and we want to find how much more, we need to subtract Alyssa's amount from Alyanna's amount
Therefore, Alyanna has 11 more cookies than Alyssa.
Help pleaseeee helpp!!
Answer:
D
Step-by-step explanation:
i did the math
A lookout tower above a canyon is 4 meters above ground level. The depth of the canyon is 16 meters below ground level. If 0 represents ground level, which number sentence correctly compares their distances above and below ground level?
A) 4<-16
B)4>-16
C)-4<16
D)-4>16
Answer:
B
Step-by-step explanation:
4 meters above. So 4 will not be negative, this eliminates C and D.
16 is definitely negative. So that eliminates C and D again.
< the number on the left of this is smaller than the right
> the number of the right of this is bigger than the left
4 is larger than -16
4>-16
B
You got 7 questions correct and 3 questions wrong on your test. What was your score as a percent?
Answer:
70%
Step-by-step explanation:
Correct/total questions --> Formula for this problem
Correct questions - 7
Total questions - 10
So, 7/10=70%!
Hope this helps you!
Bernard typically runs x km/hour. While he was sick, he only ran 41. 5 km/hour. What equation represents that the difference in his speeds is 13. 5 km/hour? x – 41. 5 = 13. 5 41. 5 x = 13. 5 13. 5 – x = 41. 5 13. 5 – 41. 5 = x.
Step-by-step explanation:
Typical speed of Bernard= x km/hr
Bernard's speed while sick= 41.5 km/hr
the difference in the speed=13.5 km/hr
the equation representing the difference will be:
x-41.5=13.5 km/hr
can you simplify 4(-5+100)
Can someone please help me with all of these. And thank you.
Answer/Step-by-step explanation:
1. x = -3.6
Add 1 on both sides.
18x = 23x + 18
Subtract 23x on both sides.
Combine like terms.
Divide the answer.
-5x = 18
x = -3.6
2. x = 11/3 (2.66666...)
Add 5 on both sides.
6x = 3x + 11
Subtract 3x on both sides.
Combine like terms.
Divide the answer.
3x = 11
x = 11/3
3. x = 23
Subtract 12 on both sides.
5x = 6x - 23
Subtract 6x on both sides.
Combine like terms.
Divide the answer.
-x = -23
x=23
(that's all.)
actually what is this?
Answer:
x²-25=?
Step-by-step explanation:
x² is known as a positive number.A positive number is any number more than 0
so we can there fore assume it's 4 so 4-25 no we can't so we divide
4÷25=0.16 it is a decimal.
2) It takes me 25 minutes to drive to school in the morning and 20 minutes to drive home after
school if those times stay the same every day, how much time do I spend driving to and from school
in a week?
Answer:
225 minutes if school is 5 days a week.
Step-by-step explanation:
20+25=45. 45x5=225
verify that the segment lengths form a triangle. is the triangle acute, right, or obtuse?
bc Answer: They form an obtuse triangle
Step-by-step explanation:
the length of one side must be greater than the difference and less than the sum of the lengths of the other two sides. In this case the third side must be greater than 3 and less than 31. 3(squareroot) 55 is 22.25 so it fits.
amelia mom baked 48 cookies after amelia and her friends walk in the kitchen there are 18 cookies left
And here’s the second one for the Brainly
Answer:
i guess it is 3a^3-20a^2+16a-24
Cost of 1 dozen peaches at 65¢ each.
Answer:
780¢
Step-by-step explanation:
A dozen = 12
so 12 * 65 = 780
Answer:
The answer is 780¢
Step-by-step explanation:
Given;Cost of each Peach = 65¢To Find;Cost of 1 dozen of peachesNow, we know that 1 dozen = 12
So,
65 × 12 = 780
Thus, The cost of 1 dozen of peaches is 780¢
-TheUnknownScientist 72
A clothing store is having a sale on shirts and jeans. 4 shirts and 2 pairs of jeans cost $64. 3 shirts and 3 pairs of jeans cost $72. What is the cost of one shirt? What is the cost of one pair of jeans
Answer:
Shirt:8 ; jsans:16.
Step-by-step explanation:
Let’s shorten these terms: shirt=s ; jean=j.
3s+3j=72
4s+2j=64 => =2j=64-4s => j=(64-4s):2 => j=32-2s
3s+3j=72 => (instead of j we write 32-2s=> 3s+3*(32-2s)=3s+96-6s=72
=> -3s=72-96
-3s=-24
s=24:3
s=8.
=> j=32-2s => j= 32-16 => j=16.
What is the lcm of 12 and 18
Answer:
36
Step-by-step explanation:
Hi there!
We want to find the least common multiple (LCM) of 12 and 18
One easy way to do that is to split up the numbers into one of their factor pairs, find the factor pairs between the numbers we just split apart, and then keep on going, until we only get prime numbers (numbers that only have 1 and itself as multiples)
Let's start with 12.
There are multiple ways to multiply to get to 12, but we can use 3 and 4 for example
12= 3*4
4 is 2 * 2
Substituting 2*2 for 4, 12 is equal to 2*2*3
Now for 18.
18 can also be split up multiple ways; one way would be 9 and 2
18 = 2*9
9 is 3*3
Substitute 3*3 for 9.
18=2*3*3
Now look at 2*2*3; 2 shows up twice in that string of numbers
In 2*3*3, 3 shows up twice in that string of numbers
We multiply the numbers based off of the highest number of times that they occur
In other words, we will multiply 2 * 2 and 3 * 3 together
2 * 2 * 3 * 3 = 4 * 9 = 36
The LCM of 12 and 18 is 36
Hope this helps!
See more on finding the LCM here:
https://brainly.com/question/20380514
GIVING BRAINLIEST!! someone please help me with this
Answer:
Quesnel Lake:Lake Baikal=.31
Quesnel Lake:Great Slave Lake=.82
Step-by-step explanation:
1 foot = .3048 meters
Lake Baikal: 5369 ft. = 1636.4712 m
Great Slave Lake: 2015 ft. = 614.172 m
Quesnel Lake: 506 m
Quesnel Lake:Lake Baikal
[tex]506 \div 1636.472 = .31[/tex]
Quesnel Lake:Great Slave Lake
[tex]506 \div 614.172 = .82[/tex]
HURRY PLSS (100 POINTS
Answer:
Q
Step-by-step explanation:
As it's distance versus time graph
Cyclist stopped for a drink of water means time is going on but distance is not changing .So the line should be parallel to time axisHence Q is the answer
[tex]\sf \Large \boxed{\sf Q} \\\\ In \ a\ distance-time\ graph,\ the\ horizontal\ line\ represents\ an\ object\ at\ rest.\\A \ slope\ shows\ that\ it\ is\ moving.[/tex]
Help me please it’s an easy question I guess
Answer:
The simplified fraction is
[tex] \frac{2}{9} [/tex]
Step-by-step explanation:
Finding the HCF can help a great deal, so in this case the HCF between 16 and 72 is 8.
16/8 = 2
72/8= 9
Therefore the answer is
[tex] \frac{2}{9} [/tex]