Question

the angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 26°. if the vertical distance from the bottom to the top of the mountain is 725 feet, what is the length of the gondola ride? round to the nearest foot. a. 318 feet b. 1654 feet c. 807 feet d. 652 feet

Explanation:

Step1: Set up trigonometric relation

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 26^{\circ}$, the opposite - side to the angle of elevation is the vertical distance of 725 feet, and the hypotenuse is the length of the gondola ride $l$. So, $\sin(26^{\circ})=\frac{725}{l}$.

Step2: Solve for $l$

We can rewrite the equation as $l=\frac{725}{\sin(26^{\circ})}$. Since $\sin(26^{\circ})\approx0.4384$, then $l=\frac{725}{0.4384}\approx1654$.

Answer:

B. 1654 feet