Question

A captain of a sailboat sights the top of a lighthouse at a 17-degree angle of elevation. A navigation chart shows the height of the lighthouse to be 120 m. How far is the sailboat from the lighthouse?

A) 411.76 m

B) 300 m

C) 430.76 m

D) 240 m

Answer 1

To find the distance from the sailboat to the lighthouse, one can use the given height of the lighthouse and the angle of elevation to apply the tangent function. The correct result of this trigonometric calculation is approximately 411.76 meters, so the answer is A) 411.76 m.

Step-by-step explanation:

The student is asking about finding the distance from a sailboat to a lighthouse using trigonometry principles. Given are the height of the lighthouse (120 meters) and the angle of elevation from the boat to the top of the lighthouse (17 degrees). To solve this, one can use the tangent function which relates the angle of elevation to the heights of the objects and the distance between them on the ground, defined as tangent of an angle in a right triangle is the opposite side over the adjacent side.

To calculate the distance (d) from the sailboat to the lighthouse using the tangent of the angle of elevation:

• tan(17 degrees) = 120 / d
• d = 120 / tan(17 degrees)

By performing the calculation, we find:

• d ≈ 411.76 meters

Thus, the correct answer is A) 411.76 m.