# Triangle Length Calculator

Table of contents

Relationship to calculate triangle lengthsUsing the triangle length calculatorOther related calculatorsFAQsThe **triangle length calculator** tells you the length of the third side if you enter two sides and an angle. A triangle has three sides and three angles. While we know by courtesy of the **angle sum property that the sum of interior angles is 180°**, the length of sides can be anything. To this end, you need to employ a sine law or the cosine law to relate them to each other.

*Sine* or *cosine* forms the crux of trigonometry functions that have numerous applications. One is about finding the third side or any angle for a triangle: the calculator and the accompanying text do the same. Read on to understand more about triangle length and *cosine* law.

## Relationship to calculate triangle lengths

Let's consider a triangle whose sides are `a`

, `b`

, and `c`

and angles $\alpha$, $\beta$,

$\gamma$. The sides of the triangle are related to each other with the **cosine law**:

## Using the triangle length calculator

Let ⊿ABC be a right-angled triangle having sides, `a`

and `b`

, forming the right angle, equal to `3`

and `4`

, respectively.

To find the missing side length:

- Fill in the
**angle**, $\gamma = 90°$. - Enter the length of
**side**, $a = 3$. - Input the length of
**side**, $b = 4$. - Using the triangle length calculator:

The third side of the triangle is `5`

.

### How do I find an angle of the triangle using the side?

To find the angle of the triangle opposite one of its sides, say side "a":

**Square**the**first**side, a.**Add**the**square**of the**second**side, b to it.**Subtract**the square of the**third**side, c from the sum.**Divide**the difference by the length of**second side**.**Divide**the quotient by the length of**first side**.**Divide**the quotient by`2`

.**Find the cosine inverse**of the final value to obtain the angle. Mathematically,`α = arccos ((a² + b² - c²)/(2ab))`

### What is the third side of the right triangle having two sides, 9 and 16?

The third side of the triangle is `18.36`

. Considering the third angle as `90°`

, the third side is obtainable using the cosine law. Since cos(90°) = 0, the **cosine law now translates to a Pythagoras theorem**, i.e., `c = √(9² + 16²) = 18.36`

.