Question

1. alex is standing on the ground and looks up to see a plane flying in the sky. if it is flying at an altitude of 2 miles and the distance along the ground is 5 miles to a point directly below the plane, what is the angle of elevation that alex has to look up?

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the opposite side (altitude of the plane) \(y = 2\) miles and the adjacent side (distance along the ground) \(x=5\) miles. We use the tangent function \(\tan\theta=\frac{y}{x}\).

Step2: Substitute the values

Substitute \(y = 2\) and \(x = 5\) into the tangent formula: \(\tan\theta=\frac{2}{5}=0.4\).

Step3: Find the angle

To find \(\theta\), we take the inverse tangent (arctan) of \(0.4\). Using a calculator, \(\theta=\arctan(0.4)\).

Answer:

\(\theta\approx21.8^{\circ}\)