Trigonometry Answers

A surveyor is measuring a river’s width. He uses a tree and a big rock that are on the edge of 

the river on opposite sides. After turning through an angle of 90° at the big rock, he walks 100 

meters away to his tent. He finds the angle from his walking path to the tree on the opposite side 

to be 25°. What is the width of the river?

A weight is suspended from a spring and is moving up and down in a simple harmonic motion. At start, the weight is pulled down 5 cm below the resting position, and then released. After 8 seconds, the weight reaches its highest location for the first time. Find the equation of the motion. 

the angle of elevation to the top of a 10 story skyscraper is measured to be 3 degrees from a point on the ground 2,000 feet from the building. what is the height of the skyscraper to the nearest hundreth foot.

3.)If we know the values of the sine and cosine of a and b, we can find the value of sin(A+B) by using the ____formula for sine. State the formula :

Sine(A+B)

4.)if we know the values of the sine and cosine A ana B, we can find the value of cos (A-B) by using the ____ formula for cosine. State the formula :

Cos(A-B)

5.)if we know the values of sin x and cos x, we can find the value of sin 2x by using the ____formula for sine. State the formula :sin 2x =____

6.)if we know the value of cos x and the quadrant in which x/2 lies, we can find the value of sin(x/2) by using the _____ formula for sine. State the formula:

Sin(x/2)=______

A tower, 28.4ft high must be secured with a guy wire anchored 5ft. from the base of the

tower. What angle will the guy wire make with the ground?

Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°

x=

(x+4)=

9x=

if P (2π/3) = ( -1/2 , /3/2) then cos Ø =?

Prove the following identities

(a)(cos t)(tan t)(csc t) =1

Explain the Pythagorean Theorem, its proofs and applications.

APPLICATIONS OF TRIGONOMETRY

1. An astronomer finds that the distance from planet A to galaxy B is 30 light years and the distance from A to galaxy C is 80 light years. the angle between distance AB and distance AC is measured to be 60 degree.

A. how far apart are the galaxies? (distance of galaxy B to galaxy C); and

B. Find the angle between distance AB to distance BC.

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