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Question
The given figure (not drawn to scale) shows two straight lines AB and CD. If equation of the line AB is : y = x + 1 and equation of line CD is : y = `sqrt(3)x - 1`. Write down the inclination of lines AB and CD; also, find the angle θ between AB and CD.
Solution
Equation of the line AB is y = x + 1
Slope of AB = 1
Inclination of line AB = 45° ...(Since, tan 45° = 1)
`=>` ∠RPQ = 45°
Equation of line CD is y = `sqrt(3)x - 1`
Slope of CD = `sqrt(3)`
Inclination of line CD = 60° ...(Since, tan 60° = `sqrt(3)`)
`=>` ∠DQX = 60°
∴ ∠DQP = 180° – 60° = 120°
Using angle sum property in ∆PQR,
θ = 180° – 45° – 120° = 15°
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