The Triangle Angle Calculator is a safe bet if you want to know how to find the angle of a triangle. This tool can solve your geometry issues whether you have three triangle sides, two sides, an angle, or only two angles. Theorems of triangle angles are also here. Read on to learn how to use the calculator, find answers to your questions then try it out for yourself; it’s never been easier to locate missing angles in triangles.

On the other hand you can also see our calculators from physics section, like Poisson’s Ratio Calculator, or you want to calculate how much does it cost to get your house cleaned using our House Cleaning Cost Calculator.

Triangle – Definition

A triangle is a three-sided polygon with three vertices. A vertex is a location where two or more curves, lines, or edges intersect; in the example of a triangle, the three vertices are connected by three edge segments. The vertices of a triangle are commonly referred to. As a result, a triangle with vertices a, b, and c is commonly referred to as abc.

We can characterize triangles using the lengths of their sides and internal angles. An equilateral triangle, for example, has all three sides of equal length, but an isosceles triangle has two sides of equal length. Scalene occurs when none of the sides of a triangle have equal lengths.

Types of Triangle

Triangles come in four varieties. All of them are polygons with three sides:

  1. Equilateral triangles– have three sides that are all the same length and three 60-degree angles.
  2. Isosceles– is a kind of isosceles that is characterized by two equal sides and two equal angles characterize isosceles triangles.
  3. Perpendicular– in right-angled triangles, one of the angles is a 90° angle.
  4. Scalene – there are no equal sides or angles in a scalene triangle.

Sum of Angles in a Triangle

According to the theorem, a triangle’s interior angles add up to 180 degrees:

\alpha+\beta+\gamma=180^\circ

What evidence do we have for this? Because they are opposite internal angles, the angles represented by the same Greek letters are congruent. Because they form a straight line, the sum of the three angles equals 180°. But, look, a triangle has three internal angles! As a result:

\alpha+\beta+\gamma=180^\circ

Angle Bisector of a Triangle

According to the angle bisector theorem:

An angle bisector divides the opposing side of a triangle angle into two segments proportionate to the other two triangle sides.

Or, to put it another way:

The ratio of the BD length to the DC length is equal to the length of side AB divided by the length of side AC, see following formula:

\frac {|BD|}{|DC|}=\frac {|AB|}{|AC|}

Interior and Exterior Angles of a Triangle

  • The sum of the opposite internal angles equals the exterior angle of a triangle.
  • There are six external angles in every triangle (two at each vertex are equal in measure).
  • Taken one at a time at each vertex, the outer angles always add up to 360°.
  • An external angle is added to the inner angle of the triangle to which it is adjacent.
  • The interior angles of a triangle sum up to 180 degrees. Therefore, multiply the number of triangles in the polygon by 180° to determine the sum of internal angles. Formula (n – 2) x 180 is the formula for determining the sum of interior angles.

Triangle Angle Calculator – How to use it step-by-step?

Using this calculator is very simple. It’s all over in a minute. All you have to do is enter the pages you know a, b, c or enter the pages and angles you know or any data you know, whether the height or the three sides of the triangle do not matter, and the result will come by itself. The calculator automatically extracts all the necessary information literally for your triangle. If you know sides and want to know unknown angles or area of a triangle calculator will help you or vice versa.

Triangle Angle Calculator – Example

We will now give you an example of how our calculator works. We will take the example of looking for angles. If we put that our page a = 2 cm, b = 3 and c = 4 cm, then ours is, as we have already said, just a click for solving the task and we will get solutions. For our example the answer is:

  • ∠A = α = 28.955 ° = 28 ° 57’18 ″ = 0.505 rad
  • ∠B = β = 46.567 ° = 46 ° 34’3 ″ = 0.813 rad
  • ∠C = γ = 104.478 ° = 104 ° 28’39 ″ = 1.823 rad

FAQ

Which set of angles can form a triangle?

Angles can also be useful to classify triangles. All three angles in an acute triangle are acute (less than 90 degrees). One right angle and two acute angles make form a right triangle. One obtuse angle (more than 90 degrees) plus two acute angles make up an obtuse triangle.

How many angles does a triangle have?

There are three angles of the triangle.

How to find the angles of a triangle with three sides?

Following equation (n – 2) x 180 is the formula for calculating the total measure of all internal angle unit of a polygon. The number of sides of the polygon in this example is n. The following are some examples of popular polygon total angle measurements: A triangle (a three-sided polygon) has 180 degrees sum of angles.

How to find angles of a triangle with one angle and two sides?

When we know two sides and the angle between them, we call it “SAS.” Calculate the unknown side using The Law of Cosines, then determine the lesser of the other two angles using The Law of Sines, and then add the three angles to 180° to obtain the last angle.

How do you get the third angle of a triangle when given two angles?

Finding the third angle of a triangle is straightforward if you know the measurements of the other two angles.
Simply subtract the other angle measurements from 180° to get the measurement of the third angle.