Find the angle between the lines `y-sqrt(3)x-5=0`and `sqrt(3)y-x+6=0`.

Explanation

Given lines are
`y-sqrt3x-5=0ory=sqrt3x+5" "...(i)`
`andsqrt3y-x+6=ory=(1)/(sqrt3)x-2sqrt3" "...(ii)`
Slope of line (i) is `m_(1)=sqrt3` and slope of line (ii) is `m_(2)=(1)/(sqrt3).`
The acute angle (say) `theta` between two lines is given by
`tan theta=|(m_(2)-m_(3))/(1+m_(1)m_(2))|" "...(iii)`
Putting the values of `m_(1)andm_(2)` in (iii), we get
`tan theta=|((1)/(sqrt3)-sqrt3)/(1+sqrt3xx(1)/(sqrt3))=|(1-3)/(2sqrt3)|=(1)/(sqrt3)`
Which gives `theta=30^(@).` Hence, angle between two lines is either `30^(@)or 180^(@)-30^(@)=150^(@).`