If the distance from the boat to the lighthouse is 120 meters and the angle of elevation is 40°, which of the following equations will find the height of the lighthouse? A right triangle is formed from the distance between a boat and the bottom of a lighthouse, the height of the lighthouse, and the distance from the boat to the top of the lighthouse; the angle of elevation from the boat to the top of the lighthouse is x degrees. cos 40° = 120 over 7 cos 40° = y over 120 tan 40° = 120 over 7 tan 40° = y over 120

D

Step-by-step explanation:

Please refer to the drawing (sorry, it's kind of bad. It's hard drawing on a laptop).

Anyways, the angle of elevation is simply the angle from the ground/sea level to the object. We are told that the boat is 120 meters away from the lighthouse. The angle of elevation from the boat to the (top of the) lighthouse is 40°. And, we are told that a right triangle is formed.

With this, we can use tangent. This is because we have an angle, the side adjacent to the angle (120 m) and we want to find the side opposite to the angle (the height). Recall that tangent is the opposite side over the adjacent side. Therefore:

x is 40°, the opposite is the height h, and the adjacent is 120 meters. Plug in the numbers:

This is the same as option D. The variables are just different.

Further notes:

To solve, multiply both sides by 120 to cancel out the 120 on the right and isolate the h:

(Use a calculator)

Therefore, the lighthouse is approximately 101 meters tall.