Question

Ethan is watching a space shuttle launch from an observation spot 99 miles away. Find the angle of elevation from Ethan to the space shuttle, which is at a height of 0.70.7 miles.

Answer 1

The angle of elevation from Ethan to the space shuttle is approximately 0.405º.

Explanation:

Let O and A the locations observation spot and the space shuttle, respectively. BA is the height of the space shuttle from the ground. All length are measured in miles. We include a simplified geometrical representation of the situation.

Since a right triangle is formed, we can find the angle of elevation (
`\theta`), measured in sexagesimal degrees, by the following inverse trigonometrical relationship:

`\theta = \tan^(-1)\left((BA)/(OB) \right)` (1)

Where OB is the distance from the observation spot to the point just below the space shuttle.

If we know that
`OB = 99\,mi` and
`BA = 0.7\,mi`, then angle of elevation from Ethan to the space shuttle is:

`\theta = \tan^(-1)\left((0.7\,mi)/(99\,mi) \right)`

`\theta \approx 0.405^(\circ)`

The angle of elevation from Ethan to the space shuttle is approximately 0.405º.