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: Calculate vertical distance

The vertical distance from the girl's height - level to the helicopter is $665 - 5=660$ feet.

Step2: Use tangent function

The tangent of the angle of depression $\theta$ is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to the angle of depression is the vertical distance $660$ feet and the adjacent side is the horizontal distance $280$ feet. So, $\tan\theta=\frac{660}{280}=\frac{33}{14}\approx2.357$.

Step3: Find the angle

We know that $\theta = \arctan(2.357)$. Using a calculator, $\theta=\arctan(2.357)\approx67^{\circ}$.

Answer:

$67^{\circ}$