To solve this problem, we can use the properties of similar triangles. When two triangles are similar, the ratios of corresponding sides are equal.

Given:

1. The smaller triangle has a height of 14 m (side $BC$) and a base of 6 m (side $AB$).
2. The larger triangle, which represents the tower with the triangle attached, has a base of 12 m (side $RP$) and an unknown height $h$ (side $QP$).

Solution:

Since the triangles are similar: $\frac{\text{Height of larger triangle}}{\text{Height of smaller triangle}} = \frac{\text{Base of larger triangle}}{\text{Base of smaller triangle}}$

Let’s set up the proportion: $\frac{h}{14} = \frac{12}{6}$

Simplify the right side: $\frac{12}{6} = 2$

So we have: $\frac{h}{14} = 2$

Now, solve for $h$ by multiplying both sides by 14: $h = 2 \times 14$ $h = 28 \, \text{m}$

Answer:

The height of the tower is 28 meters.

Would you like further details or have any questions?

Here are some related questions for practice:

1. What properties define similar triangles?
2. How can we identify corresponding sides in similar triangles?
3. What are other ways to find the height of an object using similar triangles?
4. What is the importance of the ratio in solving problems involving similar triangles?
5. How can this method be applied in real-life situations, such as measuring tall structures?

Tip: Always make sure to match corresponding sides correctly when working with similar triangles.