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

`\alpha \approx 39^(\circ)`

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 = (96\,ft)/(120\,ft)`

`\tan \alpha = (4)/(5)`

`\alpha = \tan^(-1)\left((4)/(5) \right)`

`\alpha \approx 38.660^(\circ)`

`\alpha \approx 39^(\circ)`