To solve the problem of finding the length of the brace for the closet rod holder, we can use the Pythagorean theorem, as the triangle formed by the vertical, horizontal, and brace is a right triangle.

The Pythagorean theorem states: $c^2 = a^2 + b^2$ Where:

• $c$ is the length of the hypotenuse (the brace in this case),
• $a$ and $b$ are the lengths of the other two sides (the vertical and horizontal sides).

In this case:

• $a = 16 \, \text{cm}$ (vertical side),
• $b = 29 \, \text{cm}$ (horizontal side).

We need to find $c$, the length of the brace: $c^2 = 16^2 + 29^2$ $c^2 = 256 + 841 = 1097$ $c = \sqrt{1097} \approx 33.1 \, \text{cm}$

So, the length of the brace is approximately 33.1 cm, rounded to the nearest tenth.

Would you like more details or have any questions? Here are some related questions:

1. How would the brace length change if the horizontal side was longer?
2. What is the angle between the brace and the horizontal side?
3. How can we calculate the area of this right triangle?
4. What are other examples where the Pythagorean theorem is useful?
5. Can you use trigonometry to find other angles in this triangle?

Tip: Always check whether a triangle is a right triangle before using the Pythagorean theorem!