A person 5 ft. tall is standing near a building 30 ft. high. If the length of the person’s shadow is 3 ft., what is the length of the shadow of the building?
We can set up a proportion to solve this problem. Let's call the length of the building's shadow x. Since the height of the building is 30 ft. and the length of the person's shadow is 3 ft., the person's height must be 5 ft * (x/3 ft) = 5x/3 ft. Since the person's height and the building's height form similar triangles with the lengths of their shadows, we can set up the following proportion: 5x/3 ft / 5 ft = 30 ft / x ft. We can cross multiply and solve for x:
5x/3 ft = (30 ft * 5 ft) / 3 ft
5x = 150 ft * ft / 3 ft
5x = 150 ft
x = 150 ft / 5
x = 30 ft
The length of the building's shadow is 30 ft. Answer: \boxed{30}.