question 28 of 40

the angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is $31^\circ$. 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. 1052 feet
b. 465 feet
c. 1751 feet
d. 773 feet

Question

question 28 of 40

the angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is $31^\circ$. 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. 1052 feet
b. 465 feet
c. 1751 feet
d. 773 feet

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Trigonometric Ratios", "Sine Ratio" ], "new_concepts": [], "current_concepts": [ "Trigonometric Ratios", "Sine Ratio", "Angle of Elevation" ] } ## Set up the trigonometric equation $$ \begin{aligned} &\theta = 31^\circ\ &\text{Opposite} = 902\text{ ft}\ &\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}\ &\sin(31^\circ) = \frac{902}{L} \end{aligned} $$ ## Solve for the length of the gondola ride $$ \begin{aligned} &L = \frac{902}{\sin(31^\circ)}\ &L \approx \frac{902}{0.515038}\ &L \approx 1751.32\text{ ft} \end{aligned} $$ ## Round to the nearest foot $$ L \approx 1751\text{ feet} $$

A. 1052 feet

B. 465 feet

C. 1751 feet

D. 773 feet

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QUESTION IMAGE

Question

Explanation:

Set up the trigonometric equation

Solve for the length of the gondola ride

Round to the nearest foot

Answer: