Law of Cosines Calculator – Two Sides and Included Angle
Find the side opposite the angle between two known sides.
Formula
c = √(a² + b² − 2ab cos C).
Side a: 3 m · Side b: 4 m · Included angle C: 90 ° · Opposite side c ≈ sqrt(((3 m)-(4 m))^2+4×(3 m)×(4 m)×sin((90 ° × 0.01745329252 rad/°)÷2)^2)
How to use
- Enter side lengths a and b.
- Enter the included angle C between them.
- Read the opposite side c in meters.
Examples
- a = 3 m, b = 4 m, C = 90° gives c = 5 m.
Frequently asked questions
Which angle is C?
It is the angle between sides a and b, opposite the unknown side c.
Can I enter 0° or 180°?
No. These produce degenerate triangles; use an angle strictly between them.
Can the sides use different units?
Yes. Both are converted to meters before calculation.
Sources
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