Triangle angles calculator

A corner is a geometric figure formed by two rays (sides of an angle) coming from one point (which is called the vertex of the angle). A plane containing both sides of an angle is divided by an angle into two areas. Each of these areas, combined with the sides of the corner, is called a flat angle (or simply an angle, if this does not cause discrepancies). One of the flat corners (usually the smaller of the two) is sometimes conventionally called internal, and the other external. Points of a flat angle that do not belong to its sides form the inner region of the flat angle.

Triangle — is a geometric figure that has three points that do not lie on the same line and three segments that pair these points in pairs. The points of a triangle are usually called its vertices, and the segments are called its sides.

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!