Question

A tourist looks out from the observation deck of the Space Needle in Seattle. The deck is at a height of 520 ft. She sees her friend on the ground below at an angle of depression of 85.6 degrees. What is the distance between the two? Round your answer to the nearest tenth of a foot.
a. 40.0 ft
b. 518.5 ft
c. 521.5 ft
d. 527.0 ft

Answer 1

Answer:

40 feet

Step-by-step explanation:

Given : The deck is at a height of 520 ft. She sees her friend on the ground below at an angle of depression of 85.6 degrees.

To Find : What is the distance between the two? Round your answer to the nearest tenth of a foot.

Solution :

Refer the attached figure

Height of deck =AB =520 ft.

Angle of depression ∠C = 85.6°

We are supposed to find length of BC i.e. distance between two.

We will use trigonometric ratios :

$tan \theta = \frac{perpendicular}{base}$

$tan 85.6^{\circ} = \frac{AB}{BC}$

$12.99615= \frac{520}{BC}$

$BC= \frac{520}{12.99615}$

$BC= 40$

Thus the distance between two is 40 feet

Answer 2

Let the distance between them be d, then
tan 85.6 = 520 / d
d = 520 / tan 85.6 = 520 / 13 = 40.0 ft