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 $21 ^ { \circ } 32 ^ { \prime }$. He then drives 1 mile $( 1 \mathrm { mile } = 5280 \mathrm { ft } )$ more and measures the angle of elevation to be $30 ^ { \circ } 9 ^ { \prime }$. Find the height of the mountain to the nearest foot.
A) $649,689 \mathrm { ft }$
B) $64,969 \mathrm { ft }$
C) $6497 \mathrm { ft }$
D) $6597 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The problem can be solved using trigonometry, specifically the tangent function, which relates the angle of elevation to the ratio of the opposite side (height of the mountain) over the adjacent side (distance from the mountain). By setting up equations for the two angles of elevation and their respective distances, and then solving these equations simultaneously, one can find the height of the mountain. The correct calculation leads to an answer of approximately 6497 feet.

Solve the Problem 21∘32′21 ^ { \circ } 32 ^ { \prime }21∘32′

Solve the Problem $21 ^ { \circ } 32 ^ { \prime }$