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Cosine rule
a² = b² + c² − 2bc cos A
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: a² = b² - 2·b·c·cos(A) + c²
- 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
- Write down the formula: a² = b² + c² − 2bc cos A.
- 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?
The formula is a² = b² + c² − 2bc cos A, where A = angle A, a = side opposite A, b = side opposite B, c = side opposite C.
What is Cosine rule when a = 7, b = 5, c = 10?
A = 0.707483 rad = 40.535802°. Substitute the values into a² = b² + c² − 2bc cos A and simplify.