Chapter 4.8, Problem 12E

Solution

To find: The height of the building.

The height of the building is approximately 71.59 ft.

Given information:

Given, to determine the height of the Louisiana-Pacific (LP) Tower, the tallest building in Conroe, Texas, a surveyor stands at a point on the ground, level with the base of the LP building. He measures the point to be 125 ft from the building’s base and the angle of elevation to the top of the building to be 29º48'.

Calculation:

The triangle representing the data is:

  

Using definitions of trigonometric functions for the triangle ABC:

  $\begin{array}{l}\tan A=\frac{\text{opposite side}}{\text{adjacent side}}\\ \tan \left(29°48\text{'}\right)=\frac{h}{125}\\ h=125\left(0.573\right)\\ h\approx 71.59\end{array}$

The height of the building is approximately 71.59 ft.

Conclusion:

The height of the building is approximately 71.59 ft.