Solve the problem.
-A police helicopter is monitoring the speed of two cars on a straight road. The helicopter is at an altitude of 4500 feet directly above the road. At one instant, the angle of elevation from the first car to the helicopter is 20°, and
The angle of elevation from the second car to the helicopter is 15°. How far apart are the two cars to the nearest
Foot?
A) 4431 ft
B) 4230 ft
C) 130 ft
D) 432 ft

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, the distance from the point directly below the helicopter (let's call this point H) to the first car (C1) can be found using the tangent of 20°: $\tan(20°) = \frac{opposite}{adjacent} = \frac{4500}{HC1}$. Solving for $HC1$, we get $HC1 = \frac{4500}{\tan(20°)}$.For the second car (C2), using the tangent of 15°: $\tan(15°) = \frac{4500}{HC2}$. Solving for $HC2$, we get $HC2 = \frac{4500}{\tan(15°)}$.The distance between the two cars is the difference between $HC2$ and $HC1$: $Distance = HC2 - HC1$.Plugging in the values and calculating, we find that the distance is approximately 4431 feet, rounding to the nearest foot.

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