# Triangle Ratio Calculator

We've built this triangle ratio calculator so that you can easily **find missing angles in triangles using ratios**. We'll discuss the math formula for triangle ratio as well as lead you through some **examples** of solving the angle ratio of a triangle.

## Triangle ratio formula

If we deal with the angle ratio of a triangle, the formula we need to remember is the one saying that the **sum of angles in a triangle is equal to the straight angle, i.e., to 180°**:

`α + β + γ = 180°`

.

How to make use of this formula? If you know your angles are in the ratio `a:b:c`

, you can write them as `ax`

, `bx`

, `cx`

, where `x`

is unknown. And, according to the above formula, we obtain:

`ax + bx + cx = 180°`

From this you can determine first the unknown `x`

, and then the angles: `ax`

, `bx`

, `cx`

. In the next section, we translate these considerations into a **step-by-step guide** on how to find missing angles in triangles using ratios.

## How do I find missing angles in triangles using ratios?

If you know the angles are in the ratio `a:b:c`

and want to determine angles:

- Write the unknown angles as
`ax`

,`bx`

,`cx`

. - Use the fact that they add up to the straight angle:
`ax + bx + cx = 180°`

. - Simplify the equation:
`(a + b + c)x = 180°`

. - Compute
`x = 180°/(a + b + c)`

. - Use
`x`

to determine the missing angles as`ax`

,`bx`

,`cx`

. - If you need the ratio of sides as well, use the law of sines.

Let's go together through examples to see how it all works in practice:

#### Example 1

The angle ratio now reads `2:3:4`

.

Write the angles as `2x`

, `3x`

, `4x`

, and write the equation for their sum as `2x + 3x + 4x = 180°`

. After simplification, we obtain `9x = 180°`

and then `x = 20°`

. As a result, `2x = 40°`

, `3x = 60°`

, `4x = 80°`

. This means our missing angles are `40°`

, `60°`

, `80°`

.

#### Example 2

Let's say the angles are in the ratio of `1:1:2`

.

We write the angles as `x`

, `x`

, `2x`

. Since their sum is `180°`

, we get: `x+x+2x = 180°`

. Hence, `4x = 180°`

, which means that `x = 45°`

. Very easily we get `2x = 90°`

, and so the missing angles are `45°`

, `45°`

, `90°`

. In particular, this is a right triangle!

## How to use this triangle ratio calculator?

Our triangle ratio calculator can work in two ways:

- enter the angle ratio and
**get the angles**; or - enter the angles and
**get the angle ratio**.

Make sure to test both possibilities!

💡 To make your life easier, if you enter two angles, our triangle ratio calculator will determine the third one automatically.

As a bonus, we'll also tell you the **ratio of side lengths**. If you need to convert the side length to angles, go to SSS triangle calculator.

## Omni tools related to angle ratio

There are two famous angle ratios for triangles: `1:2:3`

and `1:1:2`

. Both these triangles are right triangles and the latter is also isosceles (and we've met it already!). Read more about them here:

## FAQ

### How do I find the ratio of angles in a triangle?

To find the ratio of angles in a triangle:

- Take the triangle's angles:
`α`

,`β`

, and`γ`

. - Write them down as
`α:β:γ`

.**This is your ratio!**. But you may want to**simplify**it. - Divide all three numbers by their
**greatest common divisor**. - For instance, if your ratio is
`30:60:90`

, divide all three numbers by thirty:`1:2:3`

.

### What are the angles of a triangle with ratio 3 : 4 : 5?

- Write your
**angles using the given ratio**as`3x`

,`4x`

,`5x`

. - The
**sum of angles**in a triangle is the straight angle:`3x + 4x + 5x = 180°`

. **Solve**this equation for`x`

. We get`x = 15°`

.- The
**missing angles**are`3x = 45°`

,`4x =60°`

,`5x = 75°`

.

*Input data to get the results!*