Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree.
-A building 150 feet tall casts a 100 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) $55.41 ^ { \circ }$
B) $56.31 ^ { \circ }$
C) $46.40 ^ { \circ }$
D) $43.60 ^ { \circ }$

Question

Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree. 
-A building 150 feet tall casts a 100 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) $55.41 ^ { \circ }$ 
B) $56.31 ^ { \circ }$ 
C) $46.40 ^ { \circ }$ 
D) $43.60 ^ { \circ }$

Quizplus · Accepted Answer

To find the angle, we use the tangent function in trigonometry, where $\tan(\theta) = \frac{opposite}{adjacent}$. Here, the opposite side is the height of the building minus the height of the person's eyes (150 - 5 = 145 feet), and the adjacent side is the length of the shadow (100 feet). Thus, $\tan(\theta) = \frac{145}{100}$. Using a calculator to find the angle that corresponds to this tangent value gives $\theta \approx 55.41^\circ$.

Solve the Right Triangle Shown in the Figure 55.41∘55.41 ^ { \circ }55.41∘

Solve the Right Triangle Shown in the Figure $55.41 ^ { \circ }$