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.

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

Step-by-step 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 (), measured in sexagesimal degrees, by the following inverse trigonometrical relationship:

(1)

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

If we know that and , then angle of elevation from Ethan to the space shuttle is:

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