Question

A surveyor stands $100\text{feet}$ from a building and sights the top of the building at a $55°$ angle of elevation. Find the height of the building.

Short answer

The height of the building is $142.8\text{feet}$.

Step-by-step solution

Step 1. Write down the given information.

Considering that the height of the building is AB and the surveyor stands 100 feet away at point C from the building (AB) as shown below.

Step 2. Calculation.

Apply trigonometric ratios in triangle ABC to find the height (AB) of the building. Therefore, in triangle ABC,

$\begin{array}{c}\frac{AB}{BC}=\tan \left(55°\right)\\ AB=BC\tan \left(55°\right)\\ AB=100\tan \left(55°\right)\\ AB=142.8\text{feet}\end{array}$

Since $AB=142.8\text{feet}$, hence the height of building is $142.8\text{feet}$.

Step 3. Conclusion.

The height of the building is $142.8\text{feet}$.