Question

The hypotenuse of a 30° -60°-90° triangle has a length of 12cm. What length could the leg be?

Answer 1

In a 30°-60°-90° triangle, the sides are in a specific ratio. The lengths of the sides are related as follows:

- The side opposite the 30° angle (the shorter leg) is 1/2 the length of the hypotenuse.
- The side opposite the 60° angle (the longer leg) is \(\sqrt{3}/2\) times the length of the hypotenuse.

Given that the hypotenuse is 12 cm, we can find the lengths of the legs.

1. For the side opposite the 30° angle:
\[
\text{Shorter leg} = \frac{1}{2} \times \text{hypotenuse} = \frac{1}{2} \times 12 \, \text{cm} = 6 \, \text{cm}
\]

2. For the side opposite the 60° angle:
\[
\text{Longer leg} = \frac{\sqrt{3}}{2} \times \text{hypotenuse} = \frac{\sqrt{3}}{2} \times 12 \, \text{cm} = 6\sqrt{3} \, \text{cm} \approx 10.39 \, \text{cm}
\]

Therefore, the lengths of the legs could be:

- The shorter leg: **6 cm**
- The longer leg: **6√3 cm (approximately 10.39 cm)**

So the possible lengths for the legs of the triangle are **6 cm** and **6√3 cm**.