# Triangle angles calculator

## Angle

## Triangle

## Triangle angles

A triangle is a three-sided polygon. The sum of the angles of a triangle is always 180 degrees. Each angle in a triangle is called a vertex angle, and there are three vertex angles in every triangle. Knowing the measures of the vertex angles of a triangle can help you solve many mathematical problems involving triangles.

## Triangle Angles Formula

The formula for finding the measure of each vertex angle in a triangle is:

**Angle(γ) = 180⁰ - (Angle(α) + Angle(β))**

For example, if two of the vertex angles in a triangle are 40 degrees and 60 degrees, the formula would be:

**Angle = 180 - 60 - 40 = 80 degrees**

Also triangle angles can be found by knowing all three sides of the triangle through the cosine theorem. **The formula is:**

cos(\alpha) = \dfrac{a^2 + c^2 - b^2}{2ac}cos(\beta) = \dfrac{a^2 + b^2 - c^2}{2ab}cos(\gamma) = \dfrac{c^2 + b^2 - a^2}{2cb}

## How to use triangle angles calculator?

Our triangle angles calculator makes it easy for you to find the measures of the vertex angles in your triangle. Simply enter the lengths of the three sides, and the calculator will automatically calculate the measure of the three angles. This tool is perfect for students, teachers, and anyone else who needs to calculate triangle angles quickly and accurately.

### Example 1:

Suppose you have a triangle with sides length of a = 30 cm b = 50 cm, and c = 60 cm. What is the measure of the angles?

cos(\alpha) = \dfrac{30^2 + 60^2 - 50^2}{2*30*60} = 0.55 \implies \alpha = 56.25^0cos(\beta) = \dfrac{30^2 + 50^2 - 60^2}{2*30*50} = −0.06 \implies \beta = 93.82^0cos(\gamma) = \dfrac{60^2 + 50^2 - 30^2}{2*60*50} = 0.86 \implies \gamma = 29.92^0

Therefore, the measure of the angle are α = 56.25, β = 93.82, and γ = 29.92 degrees.

### Example 2:

Suppose you have a triangle with sides a = 10, b = 15, c = 17. What is the measure of the triangle angles?

cos(\alpha) = \dfrac{10^2 + 17^2 - 15^2}{2*10*17} = 0.482 \implies \alpha = 61.16^0cos(\beta) = \dfrac{10^2 + 15^2 - 17^2}{2*10*15} = 0.12 \implies \beta = 83.1^0cos(\gamma) = \dfrac{17^2 + 15^2 - 10^2}{2*17*15} = 0.81 \implies \gamma = 35.73^0

Therefore, the measure of the angles are α = 61.16, β = 83.1, and γ = 35.73 degrees.

## Conclusion

In conclusion, the measures of vertex angles in a triangle are important for solving mathematical problems involving triangles. Our triangle angles calculator makes it easy to find these measures quickly and accurately. Whether you are a student, teacher, or anyone else who needs to calculate triangle angles, our calculator will help you get the job done. So, use our calculator today and make your calculations easier!

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