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 ([tex]\theta[/tex]), measured in sexagesimal degrees, by the following inverse trigonometrical relationship:
[tex]\theta = \tan^{-1}\left(\frac{BA}{OB} \right)[/tex] (1)
Where OB is the distance from the observation spot to the point just below the space shuttle.
If we know that [tex]OB = 99\,mi[/tex] and [tex]BA = 0.7\,mi[/tex], then angle of elevation from Ethan to the space shuttle is:
[tex]\theta = \tan^{-1}\left(\frac{0.7\,mi}{99\,mi} \right)[/tex]
[tex]\theta \approx 0.405^{\circ}[/tex]
The angle of elevation from Ethan to the space shuttle is approximately 0.405º.
