Question

question 8 of 33 the angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 31°. if the vertical distance from the bottom to the top of the mountain is 902 feet, what is the length of the gondola ride? round to the nearest foot. a. 773 feet b. 465 feet c. 1751 feet d. 1052 feet

Explanation:

Step1: Set up trigonometric relation

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 31^{\circ}$, the opposite - side (vertical distance) is $y = 902$ feet, and the hypotenuse is the length of the gondola ride $d$. So, $\sin31^{\circ}=\frac{902}{d}$.

Step2: Solve for $d$

We can rewrite the equation as $d=\frac{902}{\sin31^{\circ}}$. Since $\sin31^{\circ}\approx0.515$, then $d=\frac{902}{0.515}$.

Step3: Calculate the value of $d$

$d=\frac{902}{0.515}=1751.456$. Rounding to the nearest foot, $d = 1751$ feet.

Answer:

C. 1751 feet