Question

A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby castsa shadow that measures 21 feet. How tall is the building?*

Answer 1

Firstly, calculate angle m

$\begin{gathered} \tan \text{m =}\frac{12}{9}\text{ =}\frac{4}{3} \\ m\text{ = }\tan ^{-1}(\frac{4}{3}) \\ m\text{ = 53.13 degrees} \\ \end{gathered}$

To calculate x

$\begin{gathered} \tan \text{ m = }\frac{x}{12\text{ + 9}} \\ \tan \text{ 53.13 = }\frac{x}{21} \\ x\text{ = 21 x tan 53.13} \\ x\text{ = 27.99 ft} \\ x=28\text{ ft (nearest whole number)} \end{gathered}$

The height of the building is 28ft