Question

amari is standing 50 feet from the base of a building.
from where he stands, the angle formed between the top
of the building and the ground at his feet is $60^\circ$.
how tall is the building?
○ 50 ft
○ $\frac{50\sqrt{3}}{3}$ ft
○ $50\sqrt{3}$ ft
○ 100 ft

Explanation:

Step1: Define trigonometric relation

We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=60^\circ$, adjacent side = 50 ft, opposite side = building height $h$.

Step2: Substitute known values

$\tan(60^\circ) = \frac{h}{50}$
We know $\tan(60^\circ)=\sqrt{3}$, so:
$\sqrt{3} = \frac{h}{50}$

Step3: Solve for $h$

Rearrange to isolate $h$:
$h = 50 \times \sqrt{3}$

Answer:

$\boldsymbol{50\sqrt{3}}$ ft