How many feet tall?

Question

A student who is 5'6" casts a 4' shadow. How many feet tall is a nearby tree which cast a 24' shadow?

Answer 1

The student is 5.5' tall and casts a 4'

The tree has a height of h and casts a 24'.

 

Since they form two similar triangles, the ratio of their height to the length of their shadows are constant.

 

∴5.5/4 = h/24 => h = 33'.

The height of the tree is 33'