Solve the problem.
-A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed, the angle of depression to the car is $22 ^ { \circ } 50 ^ { \prime }$. When the car stops, the angle of depression is $47 ^ { \circ } 16 ^ { \prime }$. The building is 270 feet tall. How far did the car travel from when it was first noticed until it stopped? Round to the nearest foot.
A) $418 \mathrm { ft }$
B) $592 \mathrm { ft }$
C) $371 \mathrm { ft }$
D) $392 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The horizontal distance from the building to the car can be found using the tangent of the angle of depression. Initially, the distance is $270 / \tan(22^\circ 50')$, and finally, it is $270 / \tan(47^\circ 16')$. The difference between these distances gives the distance traveled by the car, which is approximately 392 feet.

Solve the Problem 22∘50′22 ^ { \circ } 50 ^ { \prime }22∘50′

Solve the Problem $22 ^ { \circ } 50 ^ { \prime }$