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Half-angle (sides)
cos(A/2) = √(s(s−a)/bc)
Where: A = angle A, a = side opposite A, b = side opposite B, c = side opposite C, s = semi-perimeter / arc length
Solved example
Given: a = 4, b = 3, c = 8, s = 6
Find: A (angle A)
- Formula: cos(A/2) = √(s·(-a + s)/(b·c))
- Rearranged for A: A = 2·acos(√(s·(-a + s)/(b·c)))
- Substitute the values: A = 2·acos(√(6·(-4 + 6)/(3·8)))
- Rearranged for A: A = -2·acos(√(-s·(a - s)/(b·c))) + 4·π
- Substitute the values: A = -2·acos(√(-6·(4 - 6)/(3·8))) + 4·π
- Result: A = 1.570796 rad = 90° ; A = 10.995574 rad = 630°
Answer: A = 1.570796 rad = 90°
Calculator
How to calculate Half-angle (sides)
- Write down the formula: cos(A/2) = √(s(s−a)/bc).
- Note the known values (a, b, c, s).
- Substitute them and simplify to find A.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Half-angle (sides)?
The formula is cos(A/2) = √(s(s−a)/bc), where A = angle A, a = side opposite A, b = side opposite B, c = side opposite C, s = semi-perimeter / arc length.
What is Half-angle (sides) when a = 4, b = 3, c = 8, s = 6?
A = 1.570796 rad = 90°. Substitute the values into cos(A/2) = √(s(s−a)/bc) and simplify.