Question

triangle theorem 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°. 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, where $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=60^\circ$, adjacent side = 50 ft, opposite side = height of building ($h$).

Step2: Substitute values into formula

$\tan(60^\circ) = \frac{h}{50}$
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 (Option: $50\sqrt{3}$ ft)