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Half-angle (sides)
sin(A/2) = √((s−b)(s−c)/bc)
Where: A = angle A, b = side opposite B, c = side opposite C, s = semi-perimeter / arc length
Solved example
Given: b = 7, c = 5, s = 10
Find: A (angle A)
- Formula: sin(A/2) = √((-b + s)·(-c + s)/(b·c))
- Rearranged for A: A = 2·asin(√(1 - s/c - s/b + s²/(b·c)))
- Substitute the values: A = 2·asin(√(10²/(5·7) - 10/7 - 10/5 + 1))
- Rearranged for A: A = -2·asin(√((b·c - b·s - c·s + s²)/(b·c))) + 2·π
- Substitute the values: A = -2·asin(√((10² - 10·5 - 10·7 + 5·7)/(5·7))) + 2·π
- Result: A = 1.427449 rad = 81.786789° ; A = 4.855737 rad = 278.213211°
Answer: A = 1.427449 rad = 81.786789°
Calculator
How to calculate Half-angle (sides)
- Write down the formula: sin(A/2) = √((s−b)(s−c)/bc).
- Note the known values (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 sin(A/2) = √((s−b)(s−c)/bc), where A = angle A, b = side opposite B, c = side opposite C, s = semi-perimeter / arc length.
What is Half-angle (sides) when b = 7, c = 5, s = 10?
A = 1.427449 rad = 81.786789°. Substitute the values into sin(A/2) = √((s−b)(s−c)/bc) and simplify.