Law of Sines & Cosines
Use these for triangles that are not right triangles.
The rules
- Law of Sines: a/sin A = b/sin B = c/sin C.
- Law of Cosines: c² = a² + b² − 2ab cos C.
- Use Law of Sines when you have an angle and its opposite side.
- Use Law of Cosines when you have two sides and the angle between them, or all three sides.
Watch out: Using the Pythagorean theorem on a triangle that has no right angle.
Worked example
In a triangle, a = 3, b = 4 and the angle between them is 90°. Find c with the Law of Cosines.
- cos 90° = 0.
- c² = 9 + 16 = 25, so c = 5.
Answer: 5
Try it yourself
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