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 =}(12)/(9)\text{ =}(4)/(3) \\ m\text{ = }\tan ^(-1)((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 = }(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