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