Triangle Ratio Calculator

Triangle Angle Ratios

If triangle angles are in ratio $a : b : c$, they satisfy $ax + bx + cx = 180°$. Solving gives $x = \frac{180}{a+b+c}$ and angles $ax$, $bx$, $cx$.

Worked Example

Ratio $2 : 3 : 4$ gives $x = \frac{180}{9} = 20°$, so angles are $40°$, $60°$, and $80°$. Ratio $1 : 1 : 2$ gives a $45°$-$45°$-$90°$ right isosceles triangle.

Frequently Asked Questions

How do I find angles from ratio 3:4:5?

$x = 180/12 = 15°$. Angles are $45°$, $60°$, and $75°$.

Can I convert known angles back to a ratio?

Yes. Enter the three angle measures. The tool simplifies them to the smallest whole-number ratio.

What ratio gives a 30-60-90 triangle?

$1 : \sqrt{3} : 2$ in side terms, or $1 : 2 : 3$ for the angle ratio $30° : 60° : 90°$.

Do angles in a triangle always sum to 180°?

Yes. That is the angle sum property used to solve every ratio problem in this calculator.

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Triangle Angle Ratios

Worked Example

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