In a right triangle, if one angle measures 30 degrees and the length of the side opposite to it is 10 units, what is the length of the hypotenuse?

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In a right triangle with a 30° angle, the triangle is a **30-60-90** triangle. The sides of a 30-60-90 triangle have a specific ratio:

- **Side opposite 30° (shortest side):** $$1$$ unit
- **Side opposite 60°:** $$\sqrt{3}$$ units
- **Hypotenuse (side opposite 90°):** $$2$$ units

Given that the side opposite the 30° angle is **10 units**, we can determine the hypotenuse as follows:

1. **Find the scale factor:**  
   Since the side opposite 30° in the standard ratio is $$1$$ unit and it's given as $$10$$ units, the scale factor is:  
   $$
   \text{Scale Factor} = \frac{10}{1} = 10
   $$
   
2. **Calculate the hypotenuse:**  
   The hypotenuse in the standard ratio is $$2$$ units. Applying the scale factor:  
   $$
   \text{Hypotenuse} = 2 \times \text{Scale Factor} = 2 \times 10 = 20 \text{ units}
   $$

Alternatively, using trigonometry:

$$
\sin(30°) = \frac{\text{Opposite Side}}{\text{Hypotenuse}} \
\sin(30°) = \frac{10}{\text{Hypotenuse}} \
0.5 = \frac{10}{\text{Hypotenuse}} \
\text{Hypotenuse} = \frac{10}{0.5} = 20 \text{ units}
$$

**Therefore, the length of the hypotenuse is 20 units.**
The hypotenuse is 20 units long.

In a right triangle, if one angle measures 30 degrees and the length of the side opposite to it is 10 units, what is the length of the hypotenuse?

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