To solve this problem, we can use the concept of similar triangles. When Anand walks 1.3 meters to the other side of the mirror and sees the top of the goalpost in the reflection, it forms two similar triangles: one formed by the goalpost and Anand's position and the other formed by the reflection and the distance from Anand's eyes to the mirror.

Steps to solve the problem:

1. Identify the key distances and variables:

   • Distance from the goalpost to Anand's position: 14.75 meters.
   • Distance from Anand to the mirror: 1.3 meters.
   • Anand's eye height: 1.45 meters.
   • Let $h$ be the height of the goalpost, which we need to find.

2. Set up the proportion based on similar triangles: The two triangles are similar because the light travels in a straight line and reflects off the mirror. Thus, we can write the following proportional equation: $\frac{\text{height of goalpost} - \text{height of Anand's eyes}}{\text{distance from goalpost to mirror}} = \frac{\text{height of Anand's eyes}}{\text{distance from Anand to mirror}}$

   Substituting the known values: $\frac{h - 1.45}{14.75} = \frac{1.45}{1.3}$

3. Solve for $h$: First, simplify the right-hand side: $\frac{1.45}{1.3} \approx 1.115$

   Now, substitute this into the equation: $\frac{h - 1.45}{14.75} = 1.115$

   Multiply both sides by 14.75 to eliminate the denominator: $h - 1.45 = 1.115 \times 14.75$ $h - 1.45 = 16.457$

   Now, add 1.45 to both sides: $h = 16.457 + 1.45 = 17.907$

4. Round the result: The height of the goalpost is approximately $\boxed{17.91}$ meters.

Final Answer:

The height of the goalpost is 17.91 meters when rounded to the nearest hundredth.

Would you like further explanation or assistance with other questions? Here are some related questions to explore:

1. How does the law of reflection apply in this scenario?
2. What would happen if the distances from Anand to the mirror or from the mirror to the goalpost were different?
3. How would the height of the goalpost change if Anand's eye height were different?
4. How can this technique of using a mirror to measure heights be applied in other situations?
5. How can trigonometry be used to solve similar problems instead of using similar triangles?

Tip: In problems involving similar triangles, ensure that the corresponding sides are proportional to each other.