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Shadows and similar triangles

Level 7 · Geometry · for questions like “A 4-foot pole casts a 5-foot shadow. A tree casts a 15-foot shadow. How tall is the tree?”

💡 The idea

At the same moment, the sun makes similar triangles: height ÷ shadow is the same for everything.

A pole and a tree with their shadows

🪜 The steps

  1. Find how many times longer the tree's shadow is.
  2. The tree is that many times taller than the pole.

✏️ Worked examples

1. Pole 4 with shadow 5, tree shadow 15: that's 3 times as long, so the tree is 4 × 3 = 12 feet.

2. Pole 6 with shadow 4, tree shadow 18: 18 ÷ 4 = 4.5 times, so the tree is 6 × 4.5 = 27 feet.

⚠️ Watch out

🎯 Try these

  1. Pole 3, shadow 2. Tree shadow 10.
  2. Pole 5, shadow 4. Tree shadow 20.
  3. Pole 2, shadow 3. Tree shadow 24.

Answers: 1) 15 2) 25 3) 16

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