Building Height Bc3747

1. **State the problem:** We need to find the height of the building (tower) given that its shadow is $30$ meters long. 2. **Identify the known values:** - Height of the pole: $2$ meters - Shadow of the pole: $4$ meters - Shadow of the building: $30$ meters - Height of the building: unknown, call it $h$ 3. **Use the property of similar triangles:** Since the pole and the building cast shadows at the same time, the triangles formed by the pole and its shadow and the building and its shadow are similar. 4. **Set up the proportion:** $$\frac{\text{height of pole}}{\text{shadow of pole}} = \frac{\text{height of building}}{\text{shadow of building}}$$ Substitute known values: $$\frac{2}{4} = \frac{h}{30}$$ 5. **Solve for $h$:** Multiply both sides by $30$: $$30 \times \frac{2}{4} = h$$ Simplify the fraction: $$30 \times \frac{\cancel{2}}{\cancel{4}} = 30 \times \frac{1}{2} = 15$$ So, $$h = 15$$ 6. **Answer:** The height of the building is $15$ meters.