From the top of the lighthouse 160 feet high the angle of depression of a boat out at sea is 24° fine to the nearest foot of the distance from the boat to the foot of the lighthouse of the foot of the lighthouse is at sea level
To find the distance from the boat to the foot of the lighthouse, we can use the tangent of the angle of depression.
Let x be the distance from the boat to the foot of the lighthouse.
We know that the height of the lighthouse is 160 feet, so the height from the boat to the top of the lighthouse is also 160 feet.
Since the angle of depression is 24°, we can calculate the tangent of this angle: tan(24°) ≈ 0.44504187.
Using the tangent, we can set up the equation:
tan(24°) = 160 / x.
Solving for x:
x = 160 / tan(24°).
x ≈ 363.1 feet.
Therefore, the distance from the boat to the foot of the lighthouse is approximately 363 feet.