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Sine rule
a/sin A = b/sin B = c/sin C = 2R
Where: A = angle A, B = base, a = side opposite A, b = side opposite B
Solved example
Given: B = 30°, a = 5, b = 10
Find: A (angle A)
- Formula: a/sin(A) = b/sin(B)
- Rearranged for A: A = asin(a·sin(B)/b)
- Substitute the values: A = asin(5·sin(30°)/10)
- Rearranged for A: A = π - asin(a·sin(B)/b)
- Substitute the values: A = π - asin(5·sin(30°)/10)
- Result: A = 0.25268 rad = 14.477512° ; A = 2.888912 rad = 165.522488°
Answer: A = 0.25268 rad = 14.477512°
Calculator
How to calculate Sine rule
- Write down the formula: a/sin A = b/sin B = c/sin C = 2R.
- Note the known values (B, a, b).
- Substitute them and simplify to find A.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Sine rule?
The formula is a/sin A = b/sin B = c/sin C = 2R, where A = angle A, B = base, a = side opposite A, b = side opposite B.
What is Sine rule when B = 30°, a = 5, b = 10?
A = 0.25268 rad = 14.477512°. Substitute the values into a/sin A = b/sin B = c/sin C = 2R and simplify.