Question

a surveyor 50 feet away from a building measures the angle from the ground to the top of the building to be 64°. what is the height of the building? feet round your answer to the nearest hundredth.

Explanation:

Step1: Set up the tangent function

Let the height of the building be \( h \). We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 64^{\circ}\) and the adjacent side is \( 50\) feet. So, \(\tan(64^{\circ})=\frac{h}{50}\).

Step2: Solve for \( h \)

Multiply both sides of the equation by \( 50\): \(h = 50\times\tan(64^{\circ})\).
Using a calculator, \(\tan(64^{\circ})\approx2.0503\). Then \(h=50\times2.0503 = 102.515\).

Answer:

\(102.52\)