Question

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?​

Answer 1

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)
• $\tan (Z)=\frac{O}{A}\\\tan (Z)=\frac{10m}{8m}=1.25$
• 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
• $\tan (X)=\frac{O}{A}\\1.25=\frac{O}{14m}\\O=(1.25)(14m)\\O=17.5m$