Triangle Calculator · Practical guide
How to Find a Missing Side With Two Angles and One Side
Two angles reveal the third, and then the Law of Sines scales the whole triangle from the one side you know.
At a glance
The Two-Step Method
First find the third angle — the three always total 180°, so subtract the two known angles. Then apply the Law of Sines, a ÷ sin A = b ÷ sin B = c ÷ sin C, to scale every side from the one you have. The ASA and AAS tabs above run both steps for you.
Interactive tool
Triangle Calculator
Enter your own values, then compare the result with the examples below.
Triangle Solution
Worked Example: A = 30°, B = 70°, Side c = 10
- Third angle: C = 180° − 30° − 70° = 80°
- Side a = 10 × sin 30° ÷ sin 80° = 10 × 0.5 ÷ 0.9848 ≈ 5.08
- Side b = 10 × sin 70° ÷ sin 80° ≈ 9.54
- Bonus — area ≈ 1/2 × a × b × sin C ≈ 23.86 square units
ASA vs AAS: What's the Difference?
ASA means the known side sits between the two known angles (like side c above); AAS means it's opposite one of them. The math is identical once the third angle is found — only the bookkeeping changes. Both tabs on this calculator handle either arrangement.
Why Three Angles Alone Aren't Enough
Angles fix a triangle's shape but not its size: a 30-60-90 triangle could be a postage stamp or a billboard. You need at least one side to pin down the scale — that's the minimum data this calculator requires.
Frequently Asked Questions
What if I know two sides and one angle instead?
Use the SAS tab if the angle is between the two sides, or the SSA tab if it isn't. Those cases use the Law of Cosines and Law of Sines respectively.
Do the angles have to be in degrees?
Yes, this calculator takes angles in degrees and returns results in degrees. Convert radians by multiplying by 180 ÷ π.
Does the Law of Sines work on right triangles?
Yes. With a 90° angle, sin 90° = 1, so the law quietly reduces to the familiar SOH-CAH-TOA relationships.
How precise are the results?
Sides display to four decimal places and angles to two, computed with full floating-point precision before rounding.