Question

1. an airplane climbs at an angle of 12, with the ground. find the horizontal distance it has traveled once it has reached an altitude of 500 feet.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the opposite side to the angle of 12° is the altitude (500 feet), and the adjacent side is the horizontal distance (\(x\)) we need to find. The tangent function relates the opposite and adjacent sides: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
So, \(\tan(12^\circ)=\frac{500}{x}\)

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{500}{\tan(12^\circ)}\)
We know that \(\tan(12^\circ)\approx0.2126\)
So, \(x=\frac{500}{0.2126}\approx2352\) (rounded to the nearest whole number)

Answer:

The horizontal distance is approximately 2352 feet.