Question

Ricardo and Sergio were standing next to each other in the backyard when Sergio challenged Ricardo to guess how tall he was. Ricardo knew his own height is 5.3 feet and when they measured their shadows, Ricardo's shadow was 11 feet long and Sergio's was 9.35 feet long. What is Sergio's height?

Answer 1

To determine Sergio's height using their shadows we will use the fact that the shadows and the persons form a right triangle, like this:

Since both angles are formed by the sun this means that the triangles are similar and therefore, their corresponding sides are at the same ratio with each other, therefore, we have:

`(S)/(9.35)=(5.3)/(11)`

We can solve for "S" by multiplying both sides by 9.35:

`S=(9.35)((5.3)/(11))`

Solving the operations:

`S=4.51`

Therefore, Sergio's height is 4.51 ft.