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We are given a rhombus with side lengths of 45.8 cm, and we need to find the distance from point \( A \) to point \( B \) (i.e., the length of one side). Additionally, we know the angle \( \theta = 20.7^\circ \).

Since the rhombus has four equal sides and the problem involves angles, we can use trigonometric principles. In this case, the diagonal \( BD \) creates two right-angled triangles: \( \triangle ABD \) and \( \triangle BCD \).

We can apply the **law of cosines** to find \( AB \), but in this case, since \( AB \) is the side of the rhombus, and all sides are known to be equal, the length of \( AB \) is simply the given side length of the rhombus.

So, \( AB = 45.8 \) cm, which is directly provided in the problem.

Would you like to explore any details or clarification on this problem? Here are some related questions to consider:

1. What is the formula for the law of cosines, and how does it work in a rhombus?
2. How can you find the length of diagonals in a rhombus?
3. What role does the given angle \( \theta \) play in solving for other parts of the rhombus?
4. How would you calculate the height of a rhombus from the base using trigonometry?
5. What are the properties of the diagonals in a rhombus and how are they related to the angles?

**Tip:** The diagonals of a rhombus bisect each other at right angles and are not equal in length. This property can be useful when calculating the area or other lengths in a rhombus.

The figure shows a rhombus whose sides are 45.8 cm long. The angle θ is 20.7°. Find the distance from A to B. Answer in units of cm.

Learn how to calculate the distance between two vertices of a rhombus when the side length and an angle are provided. This problem involves trigonometric principles, cosine law, and properties of rhombuses, making it suitable for Grades 9-11.

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