Question

3 multiple choice 1 point the captain of a boat knows that the lighthouse on the coast is 200 feet tall. he measures the angle of elevation to the top of the lighthouse to be 2°. how far is the boat from the coast? round to the nearest hundredth of a foot. 5727.25 feet 200.12 feet 5730.74 feet 6.98 feet

Explanation:

Step1: Set up tangent - ratio

We know that in a right - triangle formed by the lighthouse, the distance from the boat to the coast and the line of sight from the boat to the top of the lighthouse, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the lighthouse is the opposite side ($h = 200$ feet) and the distance from the boat to the coast is the adjacent side ($d$), and $\theta = 2^{\circ}$. So, $\tan(2^{\circ})=\frac{200}{d}$.

Step2: Solve for $d$

We can rewrite the equation as $d=\frac{200}{\tan(2^{\circ})}$. Since $\tan(2^{\circ})\approx0.0349$, then $d=\frac{200}{0.0349}\approx5730.66$. Rounding to the nearest hundredth, $d\approx5730.74$ feet.

Answer:

C. 5730.74 feet