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:

We see that the distance from the boat to the lighthouse is 120 metres, which means that the horizontal side of the triangle is 120.

We also know that the angle of elevation, x, is 40°. We want to find the height of the lighthouse, which is the vertical side of the triangle.

Since we are solving a trigonometry problem involving the two legs, we know that we will be using tangent, which is opposite / adjacent, as opposed to cosine, which is adjacent / hypotenuse. So, eliminate the first two choices.

As mentioned above, tangent is opposite / adjacent, where "opposite" is the side opposite the angle and "adjacent" is the side right next to the angle that is not the hypotenuse.

Here, the "opposite" side is the height of the lighthouse, which we want to find: y. The "adjacent" side is the distance from the boat to the lighthouse, which is given as 120 metres. The angle is 40°. We can then write:

tan(40°) = opposite / adjacent = y / 120

The answer is thus D.

~ an aesthetics lover

answer: 840

step-by-step explanation: