# Rhombus angles calculator

## Angle

## Rhombus

## Rhombus angles

Our rhombus angles calculator makes it easy for you to find the angles of your rhombus. Simply enter the length of a side and diagonal of your rhombus into the calculator, and it will automatically calculate the angles for you. This tool is perfect for students, teachers, and anyone else who needs to calculate rhombus angles quickly and accurately.

## Rhombus Angles Formula

Since the diagonals of the rhombus are mutually perpendicular, it becomes possible to find the angle of the rhombus, knowing the side and diagonal. In a right-angled triangle formed by the diagonal inside the rhombus, half the diagonals are the legs, any of which can be used, and the rhombus side becomes the hypotenuse. In such a triangle, acute angles will be half the angles of the rhombus, therefore, it will be necessary to use the properties of cosines for the transformations, which ultimately leads to the following formula.

cos(\alpha) = \dfrac{d^2}{2a^2}-1

Where d is the diagonal and a is the sidde of the rhombus.

### Examples

**Example 1:** A rhombus side length = 14 and diagonal = 23. To find the angles of this rhombus, we can use the formula:

cos(\alpha) = \dfrac{23^2}{2*14^2}-1 = 0.35 \implies \alpha = 69.54

Therefore, α angle of the rhombus is 69.54 degrees.

**Example 2:** A rhombus has side length 15cm and diagonal 27 cm. To find the angles of this rhombus, we can use the formula:

cos(\alpha) = \dfrac{27^2}{2*15^2}-1 = 0.62 \implies \alpha = 51.68

Therefore, α angle of the rhombus is 51.68 degrees.

## Conclusion

In conclusion, the rhombus is a unique shape with all sides equal in length. Our rhombus angles calculator makes it easy to find the angles of your rhombus quickly and accurately. Whether you are a student or teacher, our calculator will help you with your calculations. So, use our calculator today and make your calculations easier!

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- Diagonal
- Radius
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- Theorems