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.

Answer 1

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°