Question

If the distance from the boat to the lighthouse is 115 meters and the angle of elevation is 42°, 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.

tan 42° = y over 115
tan 42° = 115 over y
cos 42° = y over 115
cos 42° = 115 over y

Answer 1

The correct equation to find the height of the lighthouse in this scenario is:

tan 42° = height of the lighthouse (y) / 115 meters

So, the equation should be: tan 42° = y / 115

To find the height of the lighthouse in this scenario, you can use trigonometry and the tangent function (tan). Here's an explanation of why the equation tan 42° = y / 115 is the correct one:

1. You have a right triangle formed by the boat, the lighthouse, and the ground.

2. The angle of elevation, which is the angle between the line of sight from the boat to the top of the lighthouse and the horizontal ground, is given as 42°.

3. The distance from the boat to the lighthouse is 115 meters.

4. You want to find the height of the lighthouse (y).

5. The tangent (tan) of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle (in this case, the height of the lighthouse, y) to the length of the side adjacent to the angle (in this case, the distance from the boat to the lighthouse, 115 meters).

So, using the definition of the tangent function, you set up the equation:

tan 42° = y / 115

This equation allows you to solve for the height of the lighthouse (y) based on the given angle of elevation and the distance from the boat to the lighthouse.