Question

an observer (o) is located 900 feet from a building (b). the observer notices a helicopter (h) flying at a 49° angle of elevation from his line of sight. how high is the helicopter flying over the building? you must show all work and calculations to receive full credit.

Explanation:

Step1: Identify the trigonometric relation

We have a right - triangle with the 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 given values

Given $\theta = 49^{\circ}$ and the adjacent side $OB = 900$ feet. Let the height of the helicopter above the building be $h$. So, $\tan(49^{\circ})=\frac{h}{900}$.

Step3: Solve for $h$

We know that $\tan(49^{\circ})\approx1.150368$. Then $h = 900\times\tan(49^{\circ})$. So, $h=900\times1.150368 = 1035.3312$ feet.

Answer:

The helicopter is flying approximately 1035.33 feet above the building.