Solve the problem.
-A building 280 feet tall casts a 30 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 5 feet above ground level.)
A) $83.77 ^ { \circ }$
B) $83.88 ^ { \circ }$
C) $83.74 ^ { \circ }$
D) $6.26 ^ { \circ }$

Question

Quizplus · Accepted Answer

To find the angle, we can use the tangent function in trigonometry, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side is the height of the building minus the eye level of the person (280 - 5 = 275 feet), and the adjacent side is the length of the shadow (30 feet). Thus, $\tan(\theta) = \frac{275}{30}$. Solving for $\theta$ gives us $\theta = \arctan\left(\frac{275}{30}\right)$, which calculates to approximately $83.77^\circ$.

Solve the Problem 83.77∘83.77 ^ { \circ }83.77∘ B) 83.88∘83.88 ^ { \circ }83.88∘

Solve the Problem $83.77 ^ { \circ }$ B) $83.88 ^ { \circ }$