Question

suppose the angle of depression from a race car drivers eyes to the bottom of the 3 - foot high back end of the car in front of him is 18 degrees. how far apart, to the nearest foot, are their bumpers? assume the horizontal distance from the race car drivers eyes to the front of his car is 5 feet. 5 feet 7 feet 6 feet 4 feet

Explanation:

Step1: Use the tangent function

Let \(x\) be the horizontal distance from the driver's eyes to the back - end of the car in front. We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Given \(\theta = 18^{\circ}\) and the opposite side (height) \(y = 3\) feet. So \(\tan(18^{\circ})=\frac{3}{x}\). Then \(x=\frac{3}{\tan(18^{\circ})}\).
Since \(\tan(18^{\circ})\approx0.3249\), \(x=\frac{3}{0.3249}\approx9.23\) feet.

Step2: Calculate the distance between bumpers

The distance between bumpers \(d=x - 5\). Substitute \(x\approx9.23\) into the formula: \(d\approx9.23−5 = 4.23\approx4\) feet.

Answer:

4 feet