A woman wants to measure the height of a nearby building. To this end, she places a 6 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The distance between the pole and the building is175 ft, and the pole casts a shadow that is 5.5 ft long. How tall is the building? Round your answer to the nearest foot. (Note that the figure below is not drawn to scale.)

We have two triangles here.  The little one made up of the green pole and its red shadow, and the big one made up of the building and its shadow.  The sides of these triangles are in the same proportion to each other because one is just a blown up version of the other.  That gives us the following proportion to solve.

  or you might also use . 

Notice that both give you the same cross product.

I am letting x stand for the height of the building since I don’t know what that value is.

  I can solve a proportion by cross multiplying. 

This gives me 5.5x = 6 times 175.

Or 5.5x = 1050  so x, the height of the building must be

1050 divided by 5.5 or 191 ft.