To find the height of a building, Oscar stuck the end of a \(4 \frac {1}{2}\) -foot stick 6 inches straight into the ground. He measured the shadow of the stick and found it was 1 foot long. Oscar then measured the building's shadow and found it was 16 feet long.
How many feet tall is the building?
Explanation
The part of the stick that is above the ground is 4 ft 6 in – 6 in, or 4 ft high. It casts a shadow 1 ft long. The shadow of the building is 16 ft long. This creates two similar right triangles, so the ratio of the two sides of the small triangle is equal to the ratio of the corresponding sides of the large triangle. This fact lets you write the following proportion:
1:4 = 16:?
Since the shadow of the building is 16 times the shadow of the stick, the height of the building is 16 times the height of the stick: \(4 \times 16=64\)
