Final answer:
To find the distance from the boat to the lighthouse's base, use the tangent of the angle of depression, which is 24 degrees. With the lighthouse height at 160 feet, calculate distance using the formula: distance = height/tan(angle).
Step-by-step explanation:
The student's question pertains to using trigonometry to find the distance from the boat to the base of the lighthouse when the angle of depression from the lighthouse to the boat is known. As the lighthouse's height is given to be 160 feet, and the angle of depression is 24 degrees, we can use trigonometric relations to solve for the distance.
To find the distance from the boat to the base of the lighthouse (distance), we can use the tangent of the angle of depression (which is equal to the angle of elevation from the boat's perspective due to alternate interior angles):
tangent(angle) = opposite/adjacent
Therefore, using the formula:
tan(24 degrees) = height/distance
Solving for distance, we get:
distance = height/tan(24 degrees)
distance = 160 feet / tan(24 degrees)
After calculating the tangent of 24 degrees and dividing 160 feet by that value, we obtain the distance from the boat to the base of the lighthouse.