Question

A boat heading out to sea starts out at Point A, at a horizontal distance of 877 feet

from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 12°. At some later
time, the crew measures the angle of elevation from point B to be 2°. Find the
distance from point A to point B. Round your answer to the nearest foot if
necessary.

Answer 1

To find the distance from point A to point B, we can use the concept of trigonometry. Using the trigonometric function of tangent, we can set up an equation and solve for the distance.

Step-by-step explanation:

To find the distance from point A to point B, we can use the concept of trigonometry. Let's assume that the distance from point A to point B is 'x' feet. From the given information, we can form a right triangle ABC, where angle A is 12°, angle B is 90°, and angle C is 78°.

Using the trigonometric function of tangent, we can set up the following equation: tan(12°) = x / 877. Solving for x, we get x = 877 * tan(12°).

Plugging in the values, we get x ≈ 190.44 feet. Therefore, the distance from point A to point B is approximately 190 feet when rounded to the nearest foot.

Answer 2

The distance from A to B is 1152.6 ft