A 76-ft tree casts a shadow that is 100 ft long. What is the angle of elevation of the sun?
A) $36.23 ^ { \circ }$
B) $25.35 ^ { \circ }$
C) $23.37 ^ { \circ }$
D) $47.34 ^ { \circ }$
E)none of these

Question

Quizplus · Accepted Answer

The angle of elevation of the sun can be found using the tangent function in trigonometry, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side is the height of the tree (76 ft) and the adjacent side is the length of the shadow (100 ft). Thus, $\tan(\theta) = \frac{76}{100}$. To find $\theta$, we take the arctan of both sides, so $\theta = \arctan(\frac{76}{100})$. Calculating this gives an angle that is not exactly equal to any of the provided options, indicating that the correct answer is E) none of these.

A 76-Ft Tree Casts a Shadow That Is 100 Ft 36.23∘36.23 ^ { \circ }36.23∘

A 76-Ft Tree Casts a Shadow That Is 100 Ft $36.23 ^ { \circ }$