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The problem in the image involves a right triangle, often referred to as a 30°-60°-90° triangle, which has specific properties related to the lengths of its sides. The longer leg, which is opposite the 60° angle, is given as 32 cm. We need to determine the length of the shorter leg, which is opposite the 30° angle.

In a 30°-60°-90° triangle, the side lengths have the following ratios:
- The shorter leg (opposite 30°) is \( \frac{1}{\sqrt{3}} \) times the longer leg.
- The hypotenuse is twice the length of the shorter leg.

### Given:
- The longer leg = 32 cm.

### To find:
- The shorter leg (opposite the 30° angle).

### Step-by-step calculation:

Using the ratio:
\[
\text{Shorter leg} = \frac{\text{Longer leg}}{\sqrt{3}} = \frac{32}{\sqrt{3}} \, \text{cm}.
\]

Let's rationalize the denominator:
\[
\frac{32}{\sqrt{3}} = \frac{32 \times \sqrt{3}}{3} = \frac{32\sqrt{3}}{3} \, \text{cm}.
\]

### Therefore, the length of the shorter leg is:
\[
\frac{32\sqrt{3}}{3} \, \text{cm}.
\]

Now, looking at the options:
- **Option B** gives \( \frac{32}{\sqrt{3}} \), which is the correct expression.

Thus, **the correct answer is B**.

---

Would you like more details on how I performed the calculations? Here are five additional questions you might find helpful:

1. What are the properties of a 30°-60°-90° triangle?
2. How do we rationalize the denominator in a fraction like \( \frac{32}{\sqrt{3}} \)?
3. Why does the longer leg relate to the shorter leg by a factor of \( \sqrt{3} \) in this type of triangle?
4. How is the hypotenuse of a 30°-60°-90° triangle calculated based on the shorter leg?
5. Can you explain the trigonometric ratios for the angles 30° and 60° in a right triangle?

**Tip:** Always remember to rationalize the denominator when dealing with square roots in the denominator of a fraction, as it's a standard practice in mathematical expressions.

If the longer leg of a drafting triangle is 32 cm, what is the length of the shorter leg?

This problem explores the properties of a 30°-60°-90° triangle, where the longer leg measures 32 cm. Using the special right triangle relationships, the shorter leg can be calculated as 32 / sqrt(3) cm. This problem is suitable for students in Grades 10-11.

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