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? cos 42° = 115/y, cos 42° = y/115, tan 42° = y/115, tan 42° = 115/y

Explanation:

Step1: Recall tangent - ratio in right - triangle

In a right - triangle, the tangent of an angle of elevation is the ratio of the opposite side to the adjacent side. Let the height of the lighthouse be $y$ and the distance from the boat to the lighthouse be 115 meters. The angle of elevation is $42^{\circ}$. The formula for the tangent of an angle $\theta$ in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute values into the tangent formula

Here, $\theta = 42^{\circ}$, the adjacent side to the $42^{\circ}$ angle is the distance from the boat to the lighthouse (115 meters), and the opposite side is the height of the lighthouse $y$. So, $\tan42^{\circ}=\frac{y}{115}$.

Answer:

$\tan42^{\circ}=\frac{y}{115}$