# Triangle Side Angle Calculator

Created by Rahul Dhari
Reviewed by Purnima Singh, PhD
Last updated: May 29, 2022

Using this Triangle side angle calculator, you can calculate the sides or angles in a triangle. A triangle is a polygon with three sides. It has three vertices and, therefore, three angles. While being pretty basic, the shape forms the crux of some advanced mathematical concepts and applications.

From this text and the accompanying calculator, you'll learn:

• What are the different ways to calculate sides and angles for a triangle?
• How to calculate the sides and angles of a triangle?

## Different ways to calculate sides and angles for a triangle

A triangle has 3 sides and three angles. Following are a few methods to calculate these values:

1. Law of cosines — The cosine of an angle is related to all three sides.
2. Law of sines — Relation between the length of the sides and the sine of the angles.
3. Pythagorean theorem — A case of cosine law for when the third angle is equal to 90°.

In addition to this, you can also use angle sum property and trigonometric ratios to find individual sides based on the data available to you.

## Using the Triangle side angle calculator

In this calculator, we'll use:

• Three sides to find angles;
• One angle and two sides to find other side and angles;
• Two angles to find the third.

Let's find the third side if one of the angles is 30°, and the sides are 4 and 6.

1. Select the given data as angle and two sides.
2. Enter the first angle, $\alpha = 30°$.
3. Insert the first side, $a = 4$.
4. Insert the second side, $b = 6$.
5. The calculator will return the third side and two angles as 7.842, 48.59°, and 101.4°, respectively.

If you find this calculator interesting, we have other triangle related calculators waiting for you:

## FAQ

### How do I find the third angle of a triangle?

To find the third angle of a triangle:

2. Subtract the sum of two angles from 180° to obtain the third angle using the angle sum property of a triangle.

### What are the angles of triangle if three sides are 4, 5, and 6?

The three angles for the triangles are 41.41°, 55.77°, and 82.82°. You can find these angles using the cosine law, such that angle, α = arccos [(b² + c² - a²)/(2bc)] = arccos[(6² + 5² - 4²)/(2 × 5 × 6)] = 41.41°. Similarly, the other two angles can be found.

Rahul Dhari
Given
angle and 2 sides
Angle selection
α α
deg
a
in
b
in
c
in
β
deg
γ
deg
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