Question

1. to find the height of a pole, a surveyor moves 50 feet away from the base of the pole and then measures the angle of elevation to the top of the pole to be 64°. his measuring tool for the angle of elevation, a transit, is 2 feet tall. what is the height of the pole?

Explanation:

Step1: Set up the tangent function

Let \(h\) be the height from the ground to the top of the pole (excluding the transit's height). We know that \(\tan\theta=\frac{opposite}{adjacent}\). Here, \(\theta = 64^{\circ}\) and the adjacent side \(x = 50\) feet. So \(\tan(64^{\circ})=\frac{h}{50}\).

Step2: Solve for \(h\)

Since \(\tan(64^{\circ})\approx2.0503\), then \(h = 50\times\tan(64^{\circ})\). Substituting the value of \(\tan(64^{\circ})\), we get \(h=50\times2.0503 = 102.515\) feet.

Step3: Add the height of the transit

The total height of the pole \(H=h + 2\). Substituting \(h = 102.515\) feet, we have \(H=102.515+2=104.515\approx104.5\) feet.

Answer:

The height of the pole is approximately \(104.5\) feet.