Question

a park ranger at the top of a 78 - meter tower sees a fire that is 390 m from the base of the tower. what is the angle of elevation? enter your answer as a number, rounded to tenths, with the appropriate unit, like this: 42.3 degrees

Explanation:

Step1: Recall tangent - ratio formula

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the tower (opposite side) is $h = 78$ meters and the distance from the base of the tower to the car (adjacent side) is $d=390$ meters. Let the angle of elevation be $\theta$. Then $\tan\theta=\frac{78}{390}$.

Step2: Calculate the value of $\tan\theta$

$\tan\theta=\frac{78}{390}=0.2$.

Step3: Find the angle $\theta$

We use the inverse - tangent function $\theta=\arctan(0.2)$. Using a calculator, $\theta=\arctan(0.2)\approx11.3^{\circ}$.

Answer:

$11.3$ degrees