Question

the angle of elevation to the top of a tall building is found to be 10 degrees from the ground at a distance of 0.9 miles from the base of the building. using this information, find the height of the building. the buildings height is __ feet.report answer accurate to 2 decimal places.

Answer 1

To determine the angle of elevation

$\begin{gathered} \text{ Using SOHCAHTOA} \\ \text{ Tan}\theta\text{ = }\frac{opp}{adj} \\ Tan10^0\text{ = }\frac{x}{0.9\text{ miles}} \\ x\text{ = 0.9 Tan10}^0 \\ x\text{ = }0.9\text{ x 0.1763} \\ x\text{ = 0.1587miles} \end{gathered}$

conversion from miles to feet =

$\begin{gathered} \text{ 1 mile = }5280foot \\ \text{ 0.9 miles = 0.1587 x 5280 f}eet \\ \text{ = }837.91\text{feet} \end{gathered}$

Hence the height of the building is 837.91 feet