Question

A boat is heading towards a lighthouse, where Shandra is watching from a vertical distance of 115 feet above the water. Shandra measures an angle of depression to the boat at point � A to be 8 ∘ ∘ . At some later time, Shandra takes another measurement and finds the angle of depression to the boat (now at point � B) to be 36 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

The distance from point A to point B is approximately 852.3 feet.

Step-by-step explanation:

In this problem, we can use the tangent function to find the distances from point A to point B. Let's start with the first measurement where the angle of depression is 8 degrees. The tangent of an angle of depression is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the vertical distance of 115 feet, and the adjacent side is the horizontal distance from point A to point B.

So, we can write the equation: tan(8) = 115 / x, where x is the distance from point A to point B. Next, we can solve this equation to find the value of x. We can rearrange the equation to isolate x by multiplying both sides by x and dividing by tan(8): x = 115 / tan(8). Using a calculator, we find that x is approximately 852.3 feet.