A park is showing a movie on the lawn. The base of the screen is 6 feet off the ground and the screen is 22 feet high (see figure).

Question

(a) Find the angles of elevation to the top of the screen from distances of 15 feet and 100 feet. (Round your answers to two decimal places.)

15 feet = _____°

100 feet = _____°

(b) You are lying on the ground and the angle of elevation to the top of the screen is 32°. How far are you from the screen? (Round your answer to two decimal places.)

_______ ft

Answer 1

Hi Aerin,

The key to answering both parts of this question is that for right triangles, we can find an unknown angle as long as we know the lengths of two of its sides.

Recall that:

sin(θ) = opposite / hypotenuse

cos(θ) = adjacent / hypotenuse

tan(θ) = opposite / adjacent

a) Since we want to find out the angle of elevation, here's how we can set up the equation to find this angle:

tan(θ) = 28/15 --> tan^-1(28/15) = θ --> θ = 61.82º from a distance of 15 feet

tan(θ) = 28/100 --> tan^-1(28/100) = θ --> θ = 15.64º from a distance of 100 feet

b) For this part, we know the angle of elevation but we do not know how far away the person is, i.e. we do not know the length of the adjacent side of this angle. However, we can still use the tangent formula as follows:

tan(32º) = 28/x

x = 28 / tan(32º) = 44.8 feet away from the screen

Answer 2

a)

tan(A) = ((22+6)/15) = 1.867 , A=61.82°

tan(B) = (28/100) = .28, B = 15.64°

b)

tan(32°) = 28/x

x = 28/tan(32°) = 28/0.625 ≈44.81 ft