Triangle Degree Calculator

Created by Purnima Singh, PhD
Reviewed by Rahul Dhari
Last updated: Sep 25, 2022

If you want to calculate the angles of a triangle, Omni's triangle degree calculator is the only tool you need.

Continue reading to learn how to calculate the degree of a triangle for several possible scenarios, i.e.,

  • When three sides are known;
  • When two angles are known; and
  • When two sides and one angle are known

You will also find an example of how to find the degree of a triangle using our tool.

What is a triangle?

A triangle is a closed curve that has three sides (aa, bb, and cc in figure 1). It consists of three vertices and three angles (α\angle \alpha, β\angle \beta, and γ \angle \gamma).

In the next section, we will try to learn how to calculate the degree of a triangle.

Triangle with sides a,b,c and angles α, β, γ
Fig 1: Triangle with sides a,b,c and angles α, β, γ

How to calculate the degree of a triangle

To calculate the degree of a triangle, we can use one of the following methods:

If the three sides are known:
We can use the law of cosines to calculate the degrees of the three angles if the sides are known. For the triangle shown in figure 1, we can find the triangle degrees using the law of cosines formula as:

α=arccos[(b2+c2a2)2bc]β=arccos[(a2+c2b2)2ac]γ=arccos[(a2+b2c2)2ab]\footnotesize \begin{align*} \alpha & = \text{arccos} \left [ \frac{(b^2+c^2-a^2)}{2bc} \right ] \\ \\ \beta & = \text{arccos} \left [ \frac{(a^2+c^2-b^2)}{2ac} \right ] \\ \\ \gamma & = \text{arccos} \left [ \frac{(a^2+b^2-c^2)}{2ab} \right ] \\ \\ \end{align*}

If two angles are known
A remarkable property of the three angles of a triangle is that the sum of the three angles of a triangle is 180 degrees. We can use this property to find the unknown degree of a triangle if two angles are known.

α+β+γ=180°α=180°(β+γ)β=180°(α+γ)γ=180°(β+α)\footnotesize \alpha + \beta + \gamma = 180\degree \\ \begin{align*} \implies \alpha & = 180\degree - ( \beta + \gamma)\\ \beta & = 180\degree - ( \alpha + \gamma) \\ \gamma & = 180\degree - ( \beta + \alpha) \end{align*}

If two sides and one angle are known
Here again, we can use the law of cosines or the law of sines to find the known degree. For example, if we know the value of the sides aa, cc, and the angle γ\gamma, using the law of sines formula we can write:

asin(α)=csin(γ)α=arcsin[asin(γ)c]β=180°(α+γ)\footnotesize \frac{a}{\text{sin} (\alpha)} = \frac{c}{\text{sin} (\gamma)} \\ \begin{align*} \implies \alpha &= \text{arcsin} \left[ \frac{a \cdot \text{sin} (\gamma)}{c} \right] \\ \beta &= 180\degree - ( \alpha + \gamma) \end{align*}

If you are interested in learning more about triangles, we recommend checking our triangle angle calculator.

How to use the Triangle degree calculator

Now let us see how to find the degree of a triangle if each of its sides measures 5 cm.

  1. Using the drop-down menu, choose 3 sides as the given option.

  2. Enter the dimensions of the three sides, aa, bb, and cc, as 4 cm each.

  3. The tool will display the degrees of the triangle (α\angle \alpha, β\angle \beta, and γ \angle \gamma) as 60°60\degree.

  4. You can also use this triangle degree calculator to find the angles of a triangle if you know either two angles or one angle and two sides.

FAQ

How to find the degree in a right triangle if one of the acute angles is known?

To find the degree in a right triangle if one of the acute angles is known, follow the given instructions:

  1. In a right triangle, one angle is 90 degrees. Hence the sum of the other two angles will be 90 degrees.

  2. Subtract the value of the known angle from 90 degrees.

  3. Congrats! You have found the degree of the unknown angle.

To what degree do the angles in a triangle add up?

According to the angle sum property of a triangle, the three interior angles in a triangle add up to 180 degrees.

What is the degree of the third angle in a triangle if two of its angles are 80° and 45°?

The third angle measures 55°. To arrive at this answer, proceed as follows:

  1. Find the sum of the two known angles, i.e., 80° + 45° = 125°.

  2. Subtract the result from 180°, i.e., 180° - 125° = 55°.

  3. You will get 55°, which is the degree of the third angle.

Purnima Singh, PhD
Given
angle and 2 sides
Angle selection
α
Triangle with sides a,b,c and angles α, β, γ






α
deg
a
in
b
in
c
in
β
deg
γ
deg
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