Question

. A tree in front of a building has a height of 16 feet and casts a shadow of 8 feet. The building casts a shadow of 32 feet. What is the height of the building?

Answer 1

Height of building is `64` feet.

Explanation:

As the sun is very distant, it's rays are parallel and all triangles formed by objects and their shadows (by joining top of the object to the end of shadow) are similar.

As such the sides are always proportional. For example in indicated problem, the shadow of `16` feet high tree is `8` feet. And as such all shadows will be half the height.

As shadow of building is `32` feet, height of building is `32×2=64` feet.

Mathematically if height of building is `x`, then `x/32=16/8=2`.

and hence `x=3×32=64` feet.