Solve the problem.
-A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed, the angle of depression to the car is $43 ^ { \circ } 15 ^ { \prime }$. When the car stops, the angle of depression is $27 ^ { \circ } 1 ^ { \prime }$. 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) $269 \mathrm { ft }$
B) $221 \mathrm { ft }$
C) $243 \mathrm { ft }$
D) $443 \mathrm { ft }$

Question

Quizplus · Accepted Answer

To find the distance the car traveled, use the tangent of the angles of depression. The tangent of an angle in a right triangle is the opposite side (height of the building) over the adjacent side (distance from the building). Calculate the distances for both angles and subtract them:  1. For $43^\circ 15'$: $\tan(43^\circ 15') = \frac{270}{x_1}$  2. For $27^\circ 1'$: $\tan(27^\circ 1') = \frac{270}{x_2}$  Solve for $x_1$ and $x_2$, then find the difference $x_2 - x_1$. The result is approximately 243 feet.

Solve the Problem 43∘15′43 ^ { \circ } 15 ^ { \prime }43∘15′

Solve the Problem $43 ^ { \circ } 15 ^ { \prime }$