To solve the problem, we will use the fact that the two triangles are similar. This means that the ratios of the corresponding sides of the two triangles are equal.

Given:

• The height $BC = 63 \, \text{cm}$
• The base $AB = 16 \, \text{cm}$
• The base $RP = 32 \, \text{cm}$

Let:

• The height of the tower $RQ = h \, \text{cm}$

Step 1: Set up the ratio of corresponding sides:

Since the triangles are similar, the ratio of their corresponding sides should be equal:

$\frac{RQ}{BC} = \frac{RP}{AB}$

Step 2: Substitute the known values:

$\frac{h}{63} = \frac{32}{16}$

Step 3: Simplify the ratio:

$\frac{32}{16} = 2$

So the equation becomes:

$\frac{h}{63} = 2$

Step 4: Solve for $h$:

Multiply both sides by 63 to find the height $h$:

$h = 2 \times 63 = 126 \, \text{cm}$

Answer:

The height of the tower $RQ$ is 126 cm.

Would you like any further details or have any other questions?

Here are some related questions to consider:

1. What is the importance of triangle similarity in geometric problems?
2. How can you verify if two triangles are similar using angle and side criteria?
3. What are some real-life applications of similar triangles?
4. How would the problem change if the tower's base was not known?
5. How can the Pythagorean theorem be applied to find the height of a triangle in different situations?

Tip: When working with similar triangles, always ensure you correctly identify the corresponding sides and angles to set up the appropriate ratio.