Ponypower2016
contestada

A power pole 10 m tall casts a shadow 8 meters long, at the same time that a building nearby casts a shadow 14 m long. How tall is the building?​

Respuesta :

SageRage

Answer:

17.5 meters

Step-by-step explanation

I included an illustration of what they are asking for.

  • Notice, since the light of the sun is coming from the same place, the shadow angles relative to the ground, X and Z, will be the same. So the triangles formed are similar
  • Use SOH CAH TOA to find the angle Z
  • This just means when you have an angle in a right triangle, in order to know whether to use Cosine, Sine or Tangent, look at what sides you have
  • We have the sides opposite (O) and adjacent (A) to angle Z, so we tangent (T)
  • [tex]\tan (Z)=\frac{O}{A}\\\tan (Z)=\frac{10m}{8m}=1.25[/tex]
  • Now since angle Z equals X, they have the same tangent value
  • So we can use that to find the building height, which it the opposite (O)
  • Don't forget to use the new adjacent 14m
  • [tex]\tan (X)=\frac{O}{A}\\1.25=\frac{O}{14m}\\O=(1.25)(14m)\\O=17.5m[/tex]
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