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°. how tall is the building? 50 ft, (50√3)/3 ft, 50√3 ft, 100 ft

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the adjacent side to the \(60^\circ\) angle is 50 feet (distance from Amari to the building), and the opposite side is the height of the building (\(h\)) we need to find. We use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\).
So, \(\tan(60^\circ)=\frac{h}{50}\).

Step2: Recall the value of \(\tan(60^\circ)\)

We know that \(\tan(60^\circ)=\sqrt{3}\). Substituting this into the equation from Step 1:
\(\sqrt{3}=\frac{h}{50}\)

Step3: Solve for \(h\)

Multiply both sides of the equation by 50 to isolate \(h\):
\(h = 50\times\sqrt{3}=50\sqrt{3}\)

Answer:

\(50\sqrt{3}\) ft (corresponding to the option " \(50\sqrt{3}\) ft")