Chapter 4.8, Problem 6E

Solution

To find: The height of the pole and the length of the wire.

The height of the pole and the length of the wire are approximately 30.09 ft and 34.08 ft respectively.

Given information:

Given, a wire stretches from the top of a vertical pole to a point on level ground 16 ft from the base of the pole. If the wire makes an angle of 62º with the ground.

Calculation:

The triangle representing the data is:

  

Using definitions of trigonometric functions for the triangle ABC:

  $\begin{array}{l}\tan A=\frac{\text{opposite side}}{\text{adjacent side}}\\ \tan 62°=\frac{h}{16}\\ h=16\left(1.88\right)\\ h\approx 30.09\end{array}$

  $\begin{array}{l}\cos A=\frac{\text{adjacent side}}{\text{hypotenuse}}\\ \cos 62°=\frac{16}{l}\\ l=\frac{16}{0.469}\\ l\approx 34.08\end{array}$

The height of the pole and the length of the wire are approximately 30.09 ft and 34.08 ft respectively.

Conclusion:

The height of the pole and the length of the wire are approximately 30.09 ft and 34.08 ft respectively.