To find the height of the building, we can use similar triangles. Since the pole and its shadow form a triangle with the sun, and the building and its shadow form a similar triangle with the same angle of sunlight, the ratios of corresponding sides of these triangles will be equal.

Given:

• Height of the pole $= 3.2 \, \text{m}$
• Shadow of the pole $= 1.64 \, \text{m}$
• Shadow of the building $= 48.5 \, \text{m}$

Let $h$ be the height of the building.

Using the similarity of the triangles: $\frac{\text{Height of Pole}}{\text{Shadow of Pole}} = \frac{\text{Height of Building}}{\text{Shadow of Building}}$

Substitute the known values: $\frac{3.2}{1.64} = \frac{h}{48.5}$

Now, solve for $h$:

1. Cross multiply: $3.2 \times 48.5 = 1.64 \times h$

2. Simplify: $155.2 = 1.64 \times h$

3. Divide by 1.64 to find $h$: $h = \frac{155.2}{1.64}$

4. Calculate $h$: $h \approx 94.7$

Rounding to the nearest meter, the height of the building is approximately $95 \, \text{m}$.

Would you like more details on any step, or do you have further questions?

Related Questions

1. How do similar triangles help in solving problems involving heights and shadows?
2. How would the height of the building change if the pole had a different height but the same shadow length?
3. How do you set up proportions in similar triangle problems with different configurations?
4. What are some real-life applications of similar triangles outside of measuring heights?
5. How would you solve this problem if you only knew the angles involved?

Tip

When working with similar triangles, always ensure that the corresponding sides are used in the ratio correctly to avoid errors in setting up proportions.