To find the height \( y \) of the lighthouse from the given distance 120 meters to the base of the lighthouse and the angle of elevation of 40°, you should use the tangent function in trigonometry.
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the lighthouse \( y \), and the adjacent side is the distance from the boat to the base of the lighthouse (120 meters).
So, the correct equation would be:
\[ \tan(40^\circ) = \frac{y}{120} \]
From the options you provided, this corresponds to:
tan 40° = y over 120
This equation can be rearranged to solve for \( y \):
\[ y = 120 \cdot \tan(40^\circ) \]
Thus, the equation tan 40° = y over 120 is the correct choice to find the height of the lighthouse.