Question

determining an angle of depression
a helicopter flies 665 feet above ground. what is the measure of the angle of depression from the helicopter to the girls line of sight? round to the nearest degree.
23°
25°
65°
67°

Explanation:

Step1: Determine the vertical and horizontal distances

The vertical distance \(y = 665 - 5=660\) feet (height of helicopter above the girl's eye - level). The horizontal distance \(x = 280\) feet.

Step2: Use the tangent function

The tangent of the angle of depression \(\theta\) (let's assume the angle of depression is equal to the angle of elevation from the girl to the helicopter due to parallel lines) is given by \(\tan\theta=\frac{y}{x}\). Substituting \(y = 660\) and \(x = 280\), we get \(\tan\theta=\frac{660}{280}=\frac{33}{14}\approx2.357\).

Step3: Find the angle

To find \(\theta\), we take the inverse - tangent (arctan) of \(2.357\). So, \(\theta=\arctan(2.357)\). Using a calculator, \(\theta\approx67^{\circ}\).

Answer:

\(67^{\circ}\)