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Roger is 5 feet tall and casts a shadow 3.5 feet long. At the same time, the flagpole outside his school casts a shadow 14 feet long. Write and solve a proportion to find the height of the flagpole.

Respuesta :

Consider the following points:

  • A = Roger's head
  • B = Roger's feet
  • C = End of Roger's shadow
  • D = Flagpole's top
  • E = Flagpole's base
  • F = End of flagpole's shadow

The triangles ABC and DEF are similar, because their are both right triangles, and we can assume that the sunlight hits both Roger and the flagpole with the same angle.

This means that the corresponding legs are in proportion, which means, in words,

[tex] \text{Roger's height } : \text{ Flagpole's height } = \text{Roger's shadow } : \text{ Flagpole's shadow} [/tex]

If you plug the known values, and let x be the flagpole's height, you have

[tex] 5 : x = 3.5 : 14 \iff x = \dfrac{14\cdot 5}{3.5} = 20 [/tex]