Question

kim is watching a satellite launch from an observation spot 6 miles away. find the angle of elevation from kim to the satellite, which is at a height of 5.7 miles. answer how to enter your answer (opens in new window) enter your answer in degrees rounded to two decimal places.

Explanation:

Step1: Recall tangent formula

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to the angle of elevation $\theta$ is the height of the satellite ($h = 5.7$ miles) and the adjacent side is the distance from the observation - spot ($d=6$ miles). So, $\tan\theta=\frac{5.7}{6}$.

Step2: Calculate the angle

We need to find $\theta$. Using the inverse - tangent function, $\theta=\arctan(\frac{5.7}{6})$.
$\theta=\arctan(0.95)$.
Using a calculator, $\theta\approx43.53^{\circ}$.

Answer:

$43.53^{\circ}$