Solve the problem.
-Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be $23 ^ { \circ } 17 ^ { \prime }$. He then drives 1 mile $\left( 1 \mathrm { mile } = 5280 \mathrm { ft } \right.$ ) more and measures the angle of elevation to be $34 ^ { \circ } 32 ^ { \prime }$. Find the height of the mountain to the nearest foot.
A) $6165 \mathrm { ft }$
B) $60,645 \mathrm { ft }$
C) $606,452 \mathrm { ft }$
D) $6065 \mathrm { ft }$

Question

Quizplus · Accepted Answer

To solve this problem, we can use trigonometry, specifically the tangent function, which relates the angle of elevation to the height and distance from the observer to the object. Let $h$ be the height of the mountain, $d$ the initial distance from the mountain when the angle of elevation is $23^\circ 17'$, and $d + 5280$ ft (since 1 mile = 5280 ft) the distance after Bob drives 1 mile further.From the first measurement, $\tan(23^\circ 17') = \frac{h}{d}$.From the second measurement, $\tan(34^\circ 32') = \frac{h}{d - 5280}$.Solving these equations simultaneously allows us to find $h$, the height of the mountain. The calculations lead to a height of approximately 6065 feet, making choice D the correct answer.

Solve the Problem 23∘17′23 ^ { \circ } 17 ^ { \prime }23∘17′

Solve the Problem $23 ^ { \circ } 17 ^ { \prime }$