Question

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).

Answer 1

Answer:

A. 61.82°;

15.64°

B. 33.37°

Step-by-step explanation:

A.

✍️Angle of elevation from 15 ft:

A right triangle is formed. Apply trigonometric ratios formula to find the angle of elevation from 15 ft.

Thus,

Length of the side Opposite to reference angle = 22 + 6 = 28 ft

Adjacent length = 15 ft

Thus, we would have:

$tan(\theta) = \frac{opp}{adjacent} = \frac{28}{15}$

$tan(\theta) = 1.8667$

$\theta = tan^{-1}(1.8667)$

$\theta = 61.82$ (2 d.p)

✍️Angle of elevation from 100 ft:

Thus,

Length of the side Opposite to reference angle = 22 + 6 = 28 ft

Adjacent length = 100 ft

Thus, we would have:

$tan(\theta) = \frac{opp}{adjacent} = \frac{28}{100}$

$tan(\theta) = 0.28$

$\theta = tan^{-1}(0.28)$

$\theta = 15.64$ (2 d.p)

B.

✍️Distance you'd be from the screen if you lie on the ground and make an angle of elevation of 40° to the top of the screen:

Adjacent length = your distance from the screen = x

Opposite length = 22 + 6 = 28 ft

Angle of elevation = 40°

Tge trigonometric ratios formula to use would be:

$tan(\theta) = \frac{opp}{adjacent}$

Plug in the values

$tan(40) = \frac{28}{x}$

Multiply both sides by x

$x*tan(40) = 28$

Divide both sides by tan(40)

$x = \frac{28}{tan(40)}$

$x = 33.37$ (2 d.p)