Question

Find the angle between the lines whose slopes are `1/2` and 3.

Answer 1

Given that m₁ = `1/2` and m₂ = 3.

Let θ be the angle between the lines then

tan θ = `|(m_1 - m_2)/(1 + m_1m_2)|`

`= |(1/2 - 3)/(1 + 1/2 xx 3)|`

`= |((1 - 6)/2)/(1 + 3/2)|`

`= |(- 5/2)/(5/2)|`

= |- 1|

tan θ = 1

tan θ = tan 45°

∴ θ = 45°