हिन्दी में पढ़ेंHome › Formulas › Properties of a triangle › Tangent (Napier) rule
Tangent (Napier) rule
tan((B − C)/2) = ((b − c)/(b + c)) cot(A/2)
Where: A = angle A, B = base, C = angle C, b = side opposite B, c = side opposite C
Solved example
Given: B = 30°, C = 45°, b = 10, c = 4
Find: A (angle A)
- Formula: tan(B/2 - C/2) = (b - c)·cot(A/2)/(b + c)
- Rearranged for A: A = 2·acot((b + c)·tan(B/2 - C/2)/(b - c))
- Substitute the values: A = 2·acot((10 + 4)·tan(30°/2 - 45°/2)/(10 - 4))
- Result: A = -2.545514 rad = -145.847219°
Answer: A = -2.545514 rad = -145.847219°
Calculator
How to calculate Tangent (Napier) rule
- Write down the formula: tan((B − C)/2) = ((b − c)/(b + c)) cot(A/2).
- Note the known values (B, C, 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 Tangent (Napier) rule?
The formula is tan((B − C)/2) = ((b − c)/(b + c)) cot(A/2), where A = angle A, B = base, C = angle C, b = side opposite B, c = side opposite C.
What is Tangent (Napier) rule when B = 30°, C = 45°, b = 10, c = 4?
A = -2.545514 rad = -145.847219°. Substitute the values into tan((B − C)/2) = ((b − c)/(b + c)) cot(A/2) and simplify.