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This triangle is a 30-60-90 right triangle, which has known side length ratios. In a 30-60-90 triangle:

- The side opposite the 30° angle (the shortest side) is \( \frac{1}{2} \) of the hypotenuse.
- The side opposite the 60° angle is \( \frac{\sqrt{3}}{2} \) times the hypotenuse.

Given:
- Hypotenuse = 140 (opposite the 90° angle).

To find \( x \), which is the side opposite the 30° angle, we use the property of a 30-60-90 triangle:

\[
x = \frac{1}{2} \times 140 = 70
\]

So,
\[
x = 70
\]

### Answer:
**\( x = 70 \)**

Would you like further details or have any questions?

### Related Questions:
1. What are the properties of other special triangles, like 45-45-90 triangles?
2. How can you solve for unknown sides using trigonometric ratios (sin, cos, tan)?
3. How would this solution change if the hypotenuse length were different?
4. What is the significance of angle relationships in triangles?
5. How do we use similar triangles in geometric proofs?

**Tip:** For quick identification, remember the side ratios in 30-60-90 triangles: \(1 : \sqrt{3} : 2\).

Find x in the figure below, rounded to one decimal place.

Learn how to solve for x in a 30-60-90 triangle with a hypotenuse of 140, using known side length ratios. This problem covers geometry concepts and the 30-60-90 triangle theorem, suitable for students in Grades 9-10.

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