How to Find the Angle Between Sides of a Triangle Using the Law of Cosines
Learn how to calculate the angle between sides of a triangle using the Law of Cosines and inverse cosine functions in this concise guide.
0 views
To find the angle between sides of a triangle, use the Law of Cosines: c² = a² + b² - 2ab cos(C). Solve for cos(C): cos(C) = (a² + b² - c²) / (2ab). Use the inverse cosine (arccos) of the result to find angle C. This formula is useful when you know the lengths of all three sides. Alternatively, if you have the lengths of two sides and the included angle, use the Law of Sines or basic trigonometric ratios.*
FAQs & Answers
- What formula is used to find an angle when all sides of a triangle are known? The Law of Cosines formula c² = a² + b² - 2ab cos(C) is used to find the angle when all three side lengths of a triangle are known.
- How do you calculate an angle using the Law of Cosines? You solve for cos(C) = (a² + b² - c²) / (2ab) and then use the inverse cosine (arccos) function to find angle C.
- When should you use the Law of Sines instead of the Law of Cosines? The Law of Sines is typically used when you know two sides and a non-included angle or two angles and a side, while the Law of Cosines is preferred when you know all three sides or two sides and the included angle.