Question

A person who is 1.5 meters tall casts a shadow that is 8 meters long. The distance along the ground from the person (N) to the flagpole (G) is 32 meters. Find the height of the flagpole (FG) showing all calculations.

Answer 1

AA Theorem: To show two triangles are similar, it is sufficient to show that two angles of one triangle are congruent (equal) to two angles of the other triangle. All three triangles have a right angle and they all share the common angle at point S.

Flagpole is 32 meters from point S: so 1.5/8 = x/32 where x is FG
cross-multiply: 32 • 1.5 = 8x
48 = 8x
x = 6 meters

building is a total of 240 meters from point S, so: 1.5/8 = x / 240 where x is BD
cross-multiply: 240 • 1.5 = 8x
360 = 8x
x = 45 meters