Question

A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 11, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 21. Find the distance from point A to point B.

Answer 1

Let's denote the distance from point A to the lighthouse as x and the distance from point B to the lighthouse as y. We can use the tangent function to set up the following equations:

tan(11) = 111/x

tan(21) = 111/y

We want to solve for the value of y-x. We can rearrange the two equations above to solve for x and y, respectively:

x = 111/tan(11)

y = 111/tan(21)

Now we can substitute these expressions into y-x to get:

y-x = 111/tan(21) - 111/tan(11)

Using a calculator, we can evaluate this expression to get:

y-x ≈ 381.3 feet

Therefore, the distance from point A to point B is approximately 381.3 feet.