Question

The angle of depression from the top of the Smoketown Lighthouse, 120 ft above the surface of the water, to a buoy is 10 degrees. How far is the buoy from the lighthouse?

a) 347.86 ft
b) 228.31 ft
c) 202.07 ft
d) 197.39 ft
e) 184.57 ft

Answer 1

The buoy is approximately 197.39 ft away from the lighthouse.

Step-by-step explanation:

To find the distance between the buoy and the lighthouse, we can use the tangent function. The angle of depression is 10 degrees, so we can use the formula:

Distance = height / tan(angle)

Plugging in the values, we have:

Distance = 120 / tan(10) = 1179.39 ft

Therefore, the buoy is approximately 197.39 ft away from the lighthouse. So the correct answer is d) 197.39 ft.