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In the given image, we see a rhombus with all sides equal to 5 cm, and an interior angle of \(60^\circ\). To find the value of \(X\), which represents the length of the diagonal, we can use the properties of the rhombus and basic trigonometry.

### Steps to solve:
1. Since the rhombus has an internal angle of \(60^\circ\), we can observe that the diagonals bisect the internal angles of a rhombus.
2. This diagonal divides the rhombus into two congruent right-angled triangles.
3. The angle between one side and half of the diagonal is \(60^\circ / 2 = 30^\circ\).
4. The side opposite to this angle (half the diagonal) is \( \frac{X}{2} \), and the hypotenuse of this right-angled triangle is 5 cm.

#### Using trigonometry:
We can apply the sine function to find half the diagonal:
\[
\sin(30^\circ) = \frac{\frac{X}{2}}{5}
\]
Since \(\sin(30^\circ) = 0.5\), we have:
\[
0.5 = \frac{\frac{X}{2}}{5}
\]
Multiplying both sides by 5:
\[
\frac{X}{2} = 2.5
\]
Finally, multiply by 2:
\[
X = 5 \, \text{cm}
\]

Thus, the value of \(X\) is \( \boxed{5} \, \text{cm} \).

Would you like any further details or explanation?

Here are 5 related questions you might find useful:
1. How do you find the area of a rhombus using its diagonals?
2. How do the properties of rhombuses differ from squares and rectangles?
3. What are other ways to calculate diagonal lengths in different polygons?
4. How do the diagonals of a rhombus relate to each other?
5. Can we use Pythagoras' theorem in rhombus-based problems?

**Tip**: Remember that the diagonals of a rhombus bisect each other at right angles, which can be useful for solving many geometric problems involving rhombuses.

Find the value of X in a rhombus with 60° angles and 5 cm sides.

Learn how to find the diagonal of a rhombus with 60° angles and 5 cm sides using trigonometry and the properties of rhombuses. This step-by-step solution covers geometry and trigonometric concepts, suitable for students in Grades 9-10.

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