Question

the statue of liberty is approximately 305 feet tall. if the angle of elevation of a ship to the top of the statue is 29.6°. how far, to the nearest foot, is the ship from the statues base? feet (round to the nearest foot.)

Explanation:

Step1: Recall tangent formula

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In this case, the height of the Statue of Liberty is the opposite - side ($h = 305$ feet) and the distance from the ship to the base of the statue is the adjacent - side ($d$), and the angle of elevation $\theta=29.6^{\circ}$. So, $\tan\theta=\tan(29.6^{\circ})=\frac{h}{d}$.

Step2: Solve for $d$

We can re - arrange the formula $\tan(29.6^{\circ})=\frac{305}{d}$ to get $d=\frac{305}{\tan(29.6^{\circ})}$.
We know that $\tan(29.6^{\circ})\approx0.571$. Then $d=\frac{305}{0.571}\approx534$.

Answer:

534 feet