Question

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

Answer 1

The correct equation to find the height of the lighthouse using the given angle of elevation and distance is tan 40° = y over 120, where y represents the height of the lighthouse.

Step-by-step explanation:

To find the height of the lighthouse, we can use trigonometry, particularly the tangent function, which relates the opposite side to the adjacent side in a right-angled triangle. The distance from the boat to the lighthouse forms the adjacent side, and the height of the lighthouse is the opposite side. Given that the angle of elevation is 40° and the distance to the lighthouse is 120 meters, we can set up the following equation using the tangent function:

tan 40° = y over 120

Where y represents the height of the lighthouse. To solve for y, we rearrange the equation:

y = 120 * tan 40°

By calculating this, we can find the actual height of the lighthouse. The correct equation from the options provided is tan 40° = y over 120.