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?

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]

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?​