免费余弦定理计算器
利用余弦定理求解三角形的未知边或角。
Side C
8.8882
公式
## Law of Cosines ### Formula **c² = a² + b² - 2ab × cos(C)** **c = sqrt(a² + b² - 2ab × cos(C))** This generalizes the Pythagorean theorem. When C = 90°, cos(C) = 0, and it reduces to c² = a² + b². ### When to Use - You know two sides and the included angle (SAS) and want the third side - You know all three sides (SSS) and want an angle
计算示例
Find side c: a = 7, b = 10, angle C = 60°.
- 01c² = 49 + 100 - 2(7)(10)cos(60°)
- 02= 149 - 140 × 0.5
- 03= 149 - 70 = 79
- 04c = √79 ≈ 8.8882
常见问题
What is the law of cosines?
The law of cosines relates the three sides of a triangle to one of its angles: c² = a² + b² - 2ab cos(C). It generalizes the Pythagorean theorem.
How is this related to the Pythagorean theorem?
When angle C is 90°, cos(90°) = 0, so the formula becomes c² = a² + b², which is the Pythagorean theorem. The law of cosines works for all triangles, not just right triangles.
Can I find an angle using the law of cosines?
Yes, rearrange to: cos(C) = (a² + b² - c²) / (2ab). Then take the arccos to find the angle.
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