What is the height

Question

A building casts a shadow 48 ft long.  At the same time a 40 foot tall flagpole cast a shadow 9.6 feet long.  What is the height of the building?

Answer 1

Hi Alddan

 

The length of the shadow is a function of the object's height and the Sun ray incidence angle. If we call θ the Sun's ray incidence angle with the ground, it is the same for the pole and building, because both are illuminated by the Sun at the same time. The only difference is that the length of the projected shadow changes to keep this Sun's incidence angle θ constant.

 

In other words, to keep this Sun's incidence angle  θ constant, the pole projects a shorter shadow than the building, because the later has a higher tall than the pole. Then, the following relation between height and shadow length between pole and building is obtained:

 

tan (θ) = 40 ft/9.6 ft   for the pole

 

tan (θ) =  h / 48 ft   for the building with height "h"

 

Then:     40 / 9.6  =  h/ 48

 

Resolving for "h":    h = 40 * 48/ 9.6  = 200 ft

 

The building has a height of 200 ft