Acute angle between the lines whose slopes are $$m1=2$$,$$m2=12$$ is θ then the value of $$tan$$θ is

If θ be the acute angle between two lines having slopes $$m1$$ and $$m2$$ then $$tan$$⁡θ$$=m1$$−$$m21+m1m2Hence$$, $$tan$$θ$$=2$$−$$121+1=34$$ Therefore, $$tan$$⁡θ$$=0.75$$

Equation of line in Straight lines

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Question

Acute angle between the lines whose slopes are $m_{1} = 2, m_{2} = \frac{1}{2}$ is $θ$ then the value of $\tan θ$ is

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Solution

$If θ be the acute angle between two lines having slopes m_{1} and m_{2} then \tan θ = |\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}|$
Hence,
$\begin{matrix} \tan θ = |\frac{2 - \frac{1}{2}}{1 + 1}| \\ = \frac{3}{4} \end{matrix}$
$Therefore, \tan θ = 0.75$

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