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

Answer:

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 ($\theta$), measured in sexagesimal degrees, by the following inverse trigonometrical relationship:

$\theta = \tan^{-1}\left(\frac{BA}{OB} \right)$ (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:

$\theta = \tan^{-1}\left(\frac{0.7\,mi}{99\,mi} \right)$

$\theta \approx 0.405^{\circ}$

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