Triangle Solver
Solve a triangle from two sides and the included angle
Solve a triangle when you know two sides and the angle between them (the included angle). The calculator uses the law of cosines to find the third side, then works out the remaining angles.
Side c
4.9500
Law of cosines
Angle A
45.58°
Angle B
89.42°
How to Use This Calculator
- Enter the length of the first known side.
- Enter the length of the second known side.
- Enter the angle between them (in degrees).
- Read the third side and the other angles.
Why Use This Calculator?
- Checking geometry homework.
- Estimating an unknown distance using two measured sides and the angle at a corner.
- Laying out a triangular plot or frame.
Real-World Examples
Sides 5 and 7, included angle 60°
Using the law of cosines, the third side works out to about 6.25 units.
The law of cosines
For sides a and b with included angle C, the third side c satisfies c² = a² + b² − 2ab·cos(C). It's like a general version of Pythagoras' theorem that works for any angle, not just right angles.
Frequently Asked Questions
What's the included angle?
It's the angle formed between the two sides you entered — the corner where they meet.
Can I enter an angle over 180°?
No. A triangle's interior angles add up to 180°, so any single angle must be less than that.
Does it work in radians?
This calculator takes the angle in degrees. Convert radians to degrees first if needed.
Important Disclaimer
Solves triangles from two sides and the included angle. Results are exact for valid inputs.
Privacy
Your entries stay in your browser and aren't stored or transmitted.
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