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

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

We are asked to find the ratio of the longer leg to the hypotenuse. This ratio is:

\[
\frac{\text{longer leg}}{\text{hypotenuse}} = \frac{x\sqrt{3}}{2x} = \frac{\sqrt{3}}{2}
\]

Looking at the answer choices:
- \( B. \frac{\sqrt{3}}{2} \) is correct.

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

Would you like more details or have any other questions? Here are 5 related questions to expand this topic:

1. What is the ratio of the shorter leg to the hypotenuse in a 30-60-90 triangle?
2. How do you calculate the area of a 30-60-90 triangle if you know the shorter leg?
3. Can the Pythagorean theorem be used to verify the side lengths in a 30-60-90 triangle?
4. How do you derive the side lengths of a 30-60-90 triangle from a given hypotenuse?
5. What is the relationship between the angles and side lengths in special right triangles like 45-45-90 triangles?

**Tip:** Remember that the ratio in a 30-60-90 triangle remains constant, so once you know one side, you can easily find the others using these ratios!

Which of the following could be the ratio of the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?

Explore how to find the ratio of the longer leg to the hypotenuse in a 30-60-90 triangle. This detailed solution uses the properties of special right triangles and the formula √3 / 2. Ideal for high school geometry students.

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