Question

a radio tower is located 350 feet from a building. from a window in the building, a person determines that the angle of elevation to the top of the tower is 34° and that the angle of depression to the bottom of the tower is 32°. how tall is the tower? feet question help: video

Explanation:

Step1: Calculate the height from the window to the top of the tower

Let the height from the window to the top of the tower be \(h_1\).
We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Given \(\theta = 34^{\circ}\) and adjacent side \(x = 350\) feet.
Using the formula \(\tan34^{\circ}=\frac{h_1}{350}\), so \(h_1 = 350\times\tan34^{\circ}\).
Since \(\tan34^{\circ}\approx0.6745\), then \(h_1=350\times0.6745 = 236.075\) feet.

Step2: Calculate the height from the window to the bottom of the tower

Let the height from the window to the bottom of the tower be \(h_2\).
Given \(\theta = 32^{\circ}\) and adjacent side \(x = 350\) feet.
Using the formula \(\tan32^{\circ}=\frac{h_2}{350}\), so \(h_2 = 350\times\tan32^{\circ}\).
Since \(\tan32^{\circ}\approx0.6249\), then \(h_2=350\times0.6249=218.715\) feet.

Step3: Calculate the total height of the tower

The total height of the tower \(H=h_1 + h_2\).
\(H=236.075+218.715 = 454.79\) feet.

Answer:

\(454.79\)