Question

an observer (o) is located 500 feet from a school (s). the observer notices a bird (b) flying at a 39° angle of elevation from his line of sight. how high is the bird flying over the school? you must show all work and calculations to receive full credit.

Explanation:

Step1: Identify the trigonometric relation

We have a right - triangle with adjacent side to the angle of elevation and we want to find the opposite side. We use the tangent function, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute the values

Given $\theta = 39^{\circ}$ and adjacent side $= 500$ feet. Let the height of the bird $h$ be the opposite side. So, $\tan(39^{\circ})=\frac{h}{500}$.

Step3: Solve for $h$

We know that $\tan(39^{\circ})\approx 0.8098$. Then $h = 500\times\tan(39^{\circ})$.
$h=500\times0.8098 = 404.9$ feet.

Answer:

The bird is flying approximately $404.9$ feet above the school.