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Cosine rule (angle)
cos A = (b² + c² − a²) / 2bc
Where: A = angle A, a = side opposite A, b = side opposite B, c = side opposite C
Solved example
Given: a = 7, b = 5, c = 10
Find: A (angle A)
- Formula: cos(A) = (-a² + b² + c²)/(2·b·c)
- Rearranged for A: A = acos((-a² + b² + c²)/(2·b·c))
- Substitute the values: A = acos((10² + 5² - 7²)/(2·10·5))
- Rearranged for A: A = -acos((-a² + b² + c²)/(2·b·c)) + 2·π
- Substitute the values: A = -acos((10² + 5² - 7²)/(2·10·5)) + 2·π
- Result: A = 0.707483 rad = 40.535802° ; A = 5.575702 rad = 319.464198°
Answer: A = 0.707483 rad = 40.535802°
Calculator
How to calculate Cosine rule (angle)
- Write down the formula: cos A = (b² + c² − a²) / 2bc.
- Note the known values (a, b, c).
- Substitute them and simplify to find A.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Cosine rule (angle)?
The formula is cos A = (b² + c² − a²) / 2bc, where A = angle A, a = side opposite A, b = side opposite B, c = side opposite C.
What is Cosine rule (angle) when a = 7, b = 5, c = 10?
A = 0.707483 rad = 40.535802°. Substitute the values into cos A = (b² + c² − a²) / 2bc and simplify.