Question

the army corps of engineers has been instructed to measure the effectiveness of a special wireless satellite towers signal at various distances. the height of the satellite tower is 250 feet. if the towers signal reaches its equipment truck, which forms an angle of elevation of 55°, approximately how far is the truck from the base of the tower? 175 feet 357 feet 205 feet 305 feet

Explanation:

Step1: Recall tangent - function formula

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the tower is the opposite side ($h = 250$ feet) and the distance from the base of the tower to the truck is the adjacent side ($d$), and the angle of elevation $\theta = 55^{\circ}$. So, $\tan(55^{\circ})=\frac{250}{d}$.

Step2: Solve for $d$

We can re - arrange the formula to get $d=\frac{250}{\tan(55^{\circ})}$. Since $\tan(55^{\circ})\approx1.4281$, then $d=\frac{250}{1.4281}\approx175$ feet.

Answer:

175 feet