Similarity Criteria Math Example 4

Solution

1. 1
   Step 1: The sun's rays are parallel, so the angle of elevation of the sun is the same for both the tree and the stick. Both also form right angles with the ground. By AA, the two triangles formed are similar.
2. 2
   Step 2: Set up the proportion: $\frac{\text{tree height}}{\text{tree shadow}} = \frac{\text{stick height}}{\text{stick shadow}}$, so $\frac{h}{15} = \frac{2}{3}$.
3. 3
   Step 3: Solve: $h = 15 \times \frac{2}{3} = 10$ m.