Question

find the height of the tower using the information given in the illustration. the height of the tower is feet. (do not round until the final answer. then round to two decimal places as needed)

Explanation:

Step1: Use the tangent function

We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 84.669^{\circ}\) and the adjacent side \(x = 70\) ft. Let the height of the tower be \(h\). So, \(\tan(84.669^{\circ})=\frac{h}{70}\).

Step2: Solve for \(h\)

Rearrange the formula to get \(h = 70\times\tan(84.669^{\circ})\). Using a calculator, \(\tan(84.669^{\circ})\approx10.714\). Then \(h=70\times10.714 = 750.0\) (after rounding to two decimal places).

Answer:

\(750.00\)