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In a 30-60-90 right triangle, the sides follow a specific ratio relative to the angles:

- The length of the hypotenuse is the longest side.
- The shorter leg (opposite the 30° angle) is half the hypotenuse.
- The longer leg (opposite the 60° angle) is the shorter leg multiplied by \(\sqrt{3}\).

Given:
- Hypotenuse = 5 units
- Shorter leg = \(\frac{1}{2} \times 5 = 2.5\) units
- Longer leg = \(2.5 \times \sqrt{3} \approx 2.5 \times 1.732 = 4.33\) units

Therefore, the length of the long leg is approximately **4.3 units** (rounded to the nearest tenth).

Would you like further details or have any questions? Here are five related questions you might find useful:

1. How do you find the length of the short leg in a 30-60-90 triangle?
2. Can the properties of a 30-60-90 triangle be applied to other similar triangles?
3. What is the relationship between the angles and sides of any right triangle?
4. How would you calculate the area of this triangle?
5. How do the Pythagorean theorem and trigonometric ratios relate to solving right triangles?

**Tip:** In a 30-60-90 triangle, memorizing the ratio 1 : \(\sqrt{3}\) : 2 helps in quickly calculating the sides based on any given one.

Determine the length of the long leg of a 30-60 right triangle if the hypotenuse is 5.

Learn how to determine the length of the long leg in a 30-60-90 right triangle when the hypotenuse is 5 units. Using the special triangle theorem, the long leg is approximately 4.3 units.

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