Question

A 6-ft tall football player casts a 16-in. shadow. at the same time, the stadium bleachers cast a 6-ft shadow. how tall are the bleachers?

Answer 1

You need to use a ratio of height (H) to shadow length (L) to solve the first problem. It's basically a use of similar triangles, with two perpendicular sides, and with the shadow making the same angle with the vertical.

6 ft = 72 ins, so that rH/L = 72/16 = 9/2 for the player.

So the bleachers are 9/2 x 6 ft = 27 ft.

For the second problem, 9 ft = 108 in, so that the ratio of the actual linear dimensions to the plan's linear dimensions are 9ft/(1/2in) = 2 x 108 = 216.

So the stage will have dimensions 216 times larger than 1.75" by 3".

That would be 31ft 6ins x 54ft.