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The diagram shows a rectangle \( ABCD \) with diagonals intersecting at the center, and one of the angles formed by the diagonals is \( 58^\circ \). The length of the base of the rectangle \( CD \) is \( 18 \, \text{cm} \), and we need to determine the height \( x \).

### Approach:

1. The diagonals of a rectangle bisect each other at right angles.
2. Since diagonals in a rectangle are equal, triangles formed by the diagonals (like \( \triangle ABD \)) are isosceles.
3. The angle \( 58^\circ \) is part of triangle \( \triangle ABD \), and we need to find the height \( x \).

Using the fact that the diagonals form isosceles triangles and applying trigonometry:

- In \( \triangle ABD \), we know:
  - Angle at the center = \( 58^\circ \)
  - Half of the diagonal \( BD \) = \( \frac{18}{2} = 9 \, \text{cm} \).

Let me calculate \( x \) using trigonometry.The height \( x \) of the rectangle is approximately \( 14.4 \, \text{cm} \).

Would you like further explanation or have any questions?

Here are five related questions to deepen your understanding:

1. What are the properties of diagonals in a rectangle?
2. How would you calculate the diagonal of this rectangle?
3. Can this problem be solved using the Pythagorean theorem instead of trigonometry?
4. What would happen to the value of \( x \) if the angle was increased or decreased?
5. How would you approach finding \( x \) if the angle given was not in the center?

**Tip:** In any right triangle, trigonometric ratios like sine, cosine, and tangent are very useful when you know one angle and one side.

Given a rectangle ABCD with diagonals intersecting at the center and forming an angle of 58°, determine the height x. The base (CD) is 18 cm.

This problem involves finding the height of a rectangle ABCD, where the diagonals intersect at a 58° angle. With the base CD = 18 cm, solve for the height using trigonometry. Suitable for Grades 9-10.

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