Question

Ethan is watching a satellite launch from an observation spot 2 miles away. Find the angle of elevation from Ethan to the satellite, which is at a height of 4.2 miles.

Answer 1

Relative to the angle, we have the adjacent side which is equal to 2 miles, and the opposite side which is equal to 4.2 miles.

The trigonometric function that deals with opposite and adjacent side is tangent function. Therefore, to find the angle of elevation, we need to use the inverse tangent

`\begin{gathered} \theta=\tan ^(-1)\Big(\frac{\text{opposite}}{\text{adjacent}}\Big) \\ \theta=\tan ^(-1)\Big{(}(4.2)/(2)\Big{)} \\ \theta=64.53665494\degree \end{gathered}`

Rounding the angle to two decimal places, the angle of elevation is 64.54°.