Solve the problem.
-A police helicopter is monitoring the speed of two cars on a straight road. The helicopter is at an altitude of 4000 feet directly above the road. At one instant, the angle of elevation from the first car to the helicopter is 21°, and
The angle of elevation from the second car to the helicopter is 17°. How far apart are the two cars to the nearest
Foot?
A) 2520 feet
B) 2663 feet
C) 313 feet
D) 102 feet

Question

Quizplus · Accepted Answer

To find the distance between the two cars, we can use the tangent of the angles of elevation and the altitude of the helicopter. For the first car, $\tan(21°) = \frac{opposite}{adjacent} = \frac{4000}{distance_1}$, solving for $distance_1$ gives us the distance from the first car to the point directly below the helicopter. Similarly, for the second car, $\tan(17°) = \frac{4000}{distance_2}$. The distance between the two cars is $distance_1 - distance_2$. Calculating these distances and subtracting gives a result of approximately 2663 feet, rounding to the nearest foot.

Solve the Problem. -A Police Helicopter Is Monitoring the Speed of Two Cars