Question

an observer (o) is located 600 feet from a building (b). the observer notices a helicopter (h) flying at a 40° 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 relationship

We have a right - triangle where the adjacent side to the angle of elevation ($\theta = 40^{\circ}$) is the distance from the observer to the building $x = 600$ feet, and we want to find the opposite side $h$ (height of the helicopter). We use the tangent function $\tan\theta=\frac{opposite}{adjacent}$.
$$\tan\theta=\frac{h}{x}$$

Step2: Substitute the known values

Given $\theta = 40^{\circ}$ and $x = 600$ feet, we substitute into the formula:
$$\tan(40^{\circ})=\frac{h}{600}$$
Since $\tan(40^{\circ})\approx0.8391$, we can solve for $h$.
$$h = 600\times\tan(40^{\circ})$$

Step3: Calculate the value of $h$

$$h=600\times0.8391 = 503.46$$ feet

Answer:

503.46 feet