Question

A 96 foot tree casts a shadow that is 120 feet long. What is the angle of elevation of the sun? Round to the nearest degree.

Answer 1

Answer:

$\alpha \approx 39^{\circ}$

Step-by-step explanation:

Let assume that tree grows perpendicular to surface. The statement is geometrically represented in the attachment included below, which resembles a right-angled triangle. Lastly, the angle of elevation of the sun is determined with the help of the following trigonometric relationship:

$\tan \alpha = \frac{96\,ft}{120\,ft}$

$\tan \alpha = \frac{4}{5}$

$\alpha = \tan^{-1}\left(\frac{4}{5} \right)$

$\alpha \approx 38.660^{\circ}$

$\alpha \approx 39^{\circ}$