On level ground, a vertical rod 12 feet tall casts a shadow 4 feet long
On level ground, a vertical rod 12 feet tall casts a shadow 4 feet long, and at the same time a nearby vertical flagpole casts a shadow 12 feet long. How many feet tall is the flagpole?
- 4
- 8
- 12
- 20
- 36
Answer
The correct answer is E.
The vertical rod and the vertical flagpole each form a right angle with the level ground, resulting in two right triangles. The smaller right triangle (at left) is composed of the rod, the rod’s shadow, and the line of sight of the sun through the top of the rod. The larger right triangle (at right) is composed of the flagpole, the flagpole’s shadow, and the line of sight of the sun through the top of the flagpole.
Because the angle of elevation of the sun is the same for each triangle, the two triangles are similar by the Angle-Angle Similarity property. Using the ratios of corresponding sides of the similar triangles, the proportion 12/h = 4/12 is solved to find the height of the flagpole, h = 36 feet.