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 80.2°. What is the distance between the two? Round your answer to the nearest tenth of a foot.

Question

A. 89.8ft
B.512.4ft
C.526.1ft
D.527.7ft

Answer 1

To find the distance between the two, we can use trigonometry. We know the height of the observation deck (520 ft) and the angle of depression (80.2°).

Let x be the distance between the tourist and her friend on the ground.

We can set up the following trigonometric equation:

tan(80.2°) = 520 / x

Now, we can solve for x:

x = 520 / tan(80.2°)
x = 520 / 6.6161
x ≈ 78.5 ft

Therefore, the distance between the tourist and her friend on the ground is approximately 78.5 ft. Rounded to the nearest tenth of a foot, the answer is:

A. 89.8 ft.