Question

From the top of a 150 ft lighthouse at 28 degrees, the angle of depression to a ship is 21 degrees. How far is the ship from the base of the lighthouse?

A) 117.6 ft
B) 130.5 ft
C) 96.4 ft
D) 99.2 ft

Answer 1

To find the distance of the ship from the base of the lighthouse, we can use trigonometry to set up a right triangle. By using the tangent function, we can solve for the unknown side of the triangle and find that the ship is approximately 329.53 ft from the base of the lighthouse.

Step-by-step explanation:

To solve this problem, we can use trigonometry and set up a right triangle. The lighthouse is the height of the triangle, 150 ft, and the angle of depression is 21 degrees. The distance from the base of the lighthouse to the ship is the base of the triangle, which we need to find. We can use the tangent function to solve for the base:

Tan(21 degrees) = opposite / adjacent

Tan(21 degrees) = 150 ft / x ft

x ft = 150 ft / Tan(21 degrees)

x ft ≈ 329.53 ft

Therefore, the ship is approximately 329.53 ft from the base of the lighthouse.