# Triangle Side Calculator: Find the Unknown Side of a Triangle

## Side

## Triangle

## Triangle side calculator

If you need to find the length of one of the sides of a triangle, our free online triangle side calculator can help. Simply select the type and method that suits to your triangle, input the required values, and our calculator will automatically find the length of the unknown side.

## Triangle Side Formulas

There are several formulas that you can use to calculate the length of a side of a triangle.

### Through two sides and the angle

The cosine theorem in an arbitrary triangle states that one can find a side in a triangle, knowing the other two sides and the angle between them. In order to calculate the third side of the triangle, you need to extract the square root of the difference from the squares of the known sides of their double product by the cosine of the angle between them. The formula is:

b = \sqrt{a^2 + c^2 - 2ac* cos(\alpha)}

where a, b, and c are the lengths of the sides of the triangle, and α is the angle between sides a and c.

You can rearrange the formula to solve for any of the sides. For example, to solve for side c, the formula becomes:

c = \sqrt{a^2 + b^2 - 2ab* cos(\beta)}

### Isosceles triangle, through side and angle

Knowing the lateral side of the isosceles triangle and the angle at the base, you can find the third side. To do this, draw a height falling on the base, which will divide the isosceles triangle into two identical right-angled triangles, and the base also into two equal parts. Half of the base from trigonometric relations in the new triangle will be equal to the product of the side (hypotenuse) and the cosine of the angle at the base. The formula is:

b = 2acos(\alpha)

where a, and b are the lengths of the sides of the triangle, and α is the angle between sides a and b.

You can rearrange the formula to solve for side a. The formula becomes:

a = \dfrac{b}{2cos(\alpha)}

### Right triangle, through sides

In a right triangle, the side can be found using the Pythagorean theorem. The formula is:

b = \sqrt{a^2+c^2}

where a, b and c are the lengths of the sides of the triangle, b is also known as the hypotenuse.

You can rearrange the formula to solve for any of the sides. For example, to solve for side c, the formula becomes:

c = \sqrt{b^2 - a^2}

### Equilateral triangle side, through height

In an equilateral triangle, as well as in the isosceles, the side can be found through height. The formula is:

a = \dfrac{2}{\sqrt{3}}h

where a is the length of the sides of the triangle, and h is the height.

## Example Problems

Here are some examples of how to use the formulas to find the length of a side of a triangle.

### Example 1

Find the length of side c in a triangle where a = 3, b = 4, and angle α = 90°.

We can use the Law of Cosines to solve for c:

c = \sqrt{a^2 + b^2 - 2ab* cos(\alpha)}

c = \sqrt{3^2 + 4^2 - 2*3*4* cos(90^0)}

c = 5

Therefore, the length of side c is 5 units.

### Example 2

Find the length of side b in a right triangle where a = 4, c = 5.

b = \sqrt{a^2+c^2}

b = \sqrt{4^2+5^2}

b = 6.4

Therefore, the length of side b is 6.4 units.

Use our free online calculator to find the length of the unknown side of a triangle. Simply enter the required parameters, and our calculator will automatically find the length of the unknown side.

Using our calculator can save you time and prevent calculation errors. Try it out today!

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