Question: A silo’s shadow measures $45$ meters. A $3$-meter pole beside it casts a shadow of $9$ meters. How tall is the silo?
1. **State the problem:** We need to find the height of the silo given that a $3$-meter pole casts a $9$-meter shadow and the silo casts a $45$-meter shadow.
2. **Use the concept of similar triangles:** The pole and its shadow form a right triangle, and the silo and its shadow form a similar right triangle because the sun's rays create the same angle.
3. **Set up the proportion:** Height of pole / Shadow of pole = Height of silo / Shadow of silo
$$\frac{3}{9} = \frac{h}{45}$$
4. **Solve for $h$:**
Multiply both sides by $45$:
$$45 \times \frac{3}{9} = h$$
Simplify the fraction:
$$45 \times \frac{\cancel{3}}{\cancel{9}} = 45 \times \frac{1}{3} = 15$$
So,
$$h = 15$$
5. **Answer:** The silo is $15$ meters tall.