A 6-foot-tall person stands 40 feet from a tree and casts a 10-foot shadow. The end of the person's shadow lines up with the end of the tree's shadow. How tall is the tree?

• A. 20 feet
• B. 24 feet
• C. 30 feet
• D. 40 feet

Answer: (C)

Shadows from the same light source form similar right triangles with the object and its shadow, so height is proportional to shadow length. Since the two shadows end at the same point, the tree and the person share the same apex of the shadow, making their height-to-shadow-length ratios equal.

The person is 40 feet from the tree, and the tip of the person’s shadow is 10 feet beyond the person, so that point is 50 feet from the tree. That means the tree’s shadow length is 50 feet. Using the proportionality 6 (person’s height) over 10 (person’s shadow) = H (tree height) over 50 (tree shadow), we get H = 50 × (6/10) = 30 feet.