Triangle Side Calculator
Omni's triangle side calculator allows you to calculate the length of the sides of a triangle.
Continue reading to find out how to calculate the sides of a triangle for three different cases:
- If two sides and one angle are known;
- If two angles and one side are known; and
- If two sides and the perimeter are known.
You will also find an example of using the calculator to find the missing sides of a triangle.
How to find the missing side of a triangle
There are several methods to find the missing side of a triangle. Depending upon the type of given information, you can choose one of the following:
If two sides and one angle are known
If we know, the measurements of the two sides and the opposite angle to one of them, we can use the Law of Sines to find the missing side.
We can use any pair of the above ratios to solve for the third side.
On the other hand, if we know two sides and the angle between them, we can use the Law of Cosines to find the remaining side.
If two angles and one side are known
We know that the sum of the three angles of a triangle is . Hence if we know the measurement of the two angles, we can find the third angle using the equation:
Once we know the third angle, we can easily calculate the missing side using the Law of Sines mentioned above.
If two sides and the perimeter are known
This is the most simple scenario. As we know that the perimeter of a triangle is just the sum of its three sides, i.e.,
This means that if we know the measurement of two sides of a triangle (say and ), we can calculate the length of the third side as:
In the next section, we will see an example of how to calculate the sides of a triangle.
Finding the missing sides of a triangle - An example
Let us consider a triangle where , and . To calculate the triangle side lengths, we will proceed as follows:
- Using the angle sum property of a triangle, we will solve for the third angle:
- Now, we will use the Law of Sines to find the missing sides
How to use the triangle side calculator
Now let us see how we can use our calculator to find the missing side of a triangle. We will use the same example as in the previous section.
Using the drop-down menu against Given, choose the option side and 2 angles.
Now choose the option two angles + adjacent side (AAS).
Enter the dimension of angles ( and ) and side ().
The triangle side calculator will display the third angle () and the two sides ( and ).
Other triangle calculators
Make sure to check out our other calculators related to triangles:
- Centroid calculator;
- Right triangle side and angle calculator;
- Missing side of a triangle calculator;
- Triangle length calculator;
- Triangle degree calculator;
- Similar right triangles calculator;
- ABC triangle calculator;
- Is it a right triangle calculator;
- Angle of right triangle calculator; and
- Check similarity in right triangles calculator.
How to find the third side of a triangle if its two side and perimeter are given?
To find the third side of a triangle, if its two sides and perimeter are given, follow the given instructions:
Find the sum of the two sides,
Subtract the sum
a + bfrom the perimeter
Pof the triangle.
You will get the third side,
c = P - (a + b).
Calculate the triangle side lengths if two of its angles are 60° each and one of the sides is 10 cm.
The length of each side is 10 cm. Since two of the angles are 60° each, the third angle will be
180° - (60° + 60°) = 60°.
As all the three angles are equal, the triangle is an equilateral triangle. Hence, all the sides will be of the same length, i.e., 10 cm.