how do I figure out this equation

Question

how do I figure out this equation a flagpole outside Williams Academy is 28 feet high at 4 PM it cast a shadow that is 40 feet long what is the length of the shadow of a student who is 6 feet tall at 4 PM

Answer 1

This problem is much easier to solve if you draw a picture.

 

At 4 PM the Sun is in a constant position.  The flagpole is 28 feet high and its shadow is 40 feet long.  The student is 6 feet tall and his shadow is X feet long.  These right triangles have the same angle where the Sun's rays hit the ground, so we can set up a proportion of the sides (height to base):

     28 / 40  = 6 / X

 

Solving for X can be done by (1) cross multiplying, (2) inverting both sides, (3) multiplying both sides by the same amount ... Any allowed algebraic operation.  Let's cross-multiply:

       28X = 6*40

         X = 8.57 feet

         X = 8 ft 6.5 in       (this seems more practical to me because I can measure it)