flagpole height

Question

a person who is 6 feet tall walks away from a flagpole toward the tip of the shadow of the flagpole. when the person is 30 feet away from the flagpole, the tips of the persons shadow and the shadow cast by the flagpole coincide at a point 5 feet in front of the person. find the height of the flagpole

Answer 1

6/5 = F/35

6 = F/7

F = 6x7 = 42 feet

there are two right triangles formed

one has sides 6 and 5 feet

the other has sides F and 35 where F = height of the flagpole

the ratios of those 2 sides is the same, as the 2 triangles are congruent