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Angle between pair of lines
tan θ = 2√(h² − ab)/(a + b)
Where: a = Angle between pair of lines, b = b, h = h, θ = angle
Solved example
Given: b = 7, h = 5, theta = 60°
Find: a (Angle between pair of lines)
- Formula: tan(θ) = 2·√(-a·b + h²)/(a + b)
- Rearranged for a: a = (-b·(tan(θ)² + 2) + 2·√(b²·tan(θ)² + b² + h²·tan(θ)²))/tan(θ)²
- Substitute the values: a = (-7·(tan(60°)² + 2) + 2·√(5²·tan(60°)² + 7²·tan(60°)² + 7²))/tan(60°)²
- Rearranged for a: a = -(b + b/cos(θ)² + 2·√(b²/cos(θ)² - h² + h²/cos(θ)²))/tan(θ)²
- Substitute the values: a = -(7 + 7/cos(60°)² + 2·√(-5² + 5²/cos(60°)² + 7²/cos(60°)²))/tan(60°)²
- Result: a = -0.691948 ; a = -22.641385
Answer: a = -0.691948
Calculator
How to calculate Angle between pair of lines
- Write down the formula: tan θ = 2√(h² − ab)/(a + b).
- Note the known values (b, h, θ).
- Substitute them and simplify to find a.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Angle between pair of lines?
The formula is tan θ = 2√(h² − ab)/(a + b), where a = Angle between pair of lines, b = b, h = h, θ = angle.
What is Angle between pair of lines when b = 7, h = 5, theta = 60°?
a = -0.691948. Substitute the values into tan θ = 2√(h² − ab)/(a + b) and simplify.