Question

question 3
20 pts
from a point 80 feet away from the side of a building the angle of elevation (from the ground) to the top of the building is 50°. how tall is the building? round to the nearest tenth if necessary.

Explanation:

Step1: Set up the tangent - ratio

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the height of the building be $h$. The angle of elevation $\theta = 50^{\circ}$ and the adjacent side to the angle of elevation is the distance from the point to the building, which is 80 feet. So, $\tan(50^{\circ})=\frac{h}{80}$.

Step2: Solve for $h$

Multiply both sides of the equation by 80: $h = 80\times\tan(50^{\circ})$. Since $\tan(50^{\circ})\approx1.19175$, then $h=80\times1.19175 = 95.34\approx95.3$ feet.

Answer:

95.3 feet