Question

question / of 40
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. 652 feet
b. 318 feet
c. 807 feet
d. 1654 feet

Explanation:

Step1: Identify the trig - function

We know the vertical distance (opposite side) and we want to find the length of the gondola ride (hypotenuse). We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 26^{\circ}$ and the opposite side $y = 725$ feet.

Step2: Set up the equation

$\sin(26^{\circ})=\frac{725}{x}$, where $x$ is the length of the gondola ride.

Step3: Solve for $x$

$x=\frac{725}{\sin(26^{\circ})}$. Since $\sin(26^{\circ})\approx0.4384$, then $x=\frac{725}{0.4384}\approx1654$ feet.

Answer:

D. 1654 feet