Question

find the acute angle between the lines whose slope are √3 & 1/√3​

Answer 1

The acute angle between the lines is 30°

Step-by-step explanation:

The slopes of the lines are

$m_1=\sqrt3,m_2=\frac{1}{\sqrt3}$

The angle between two lines is given by

$\theta=\tan^{-1}\left |\left ( \frac{m_2-m_1}{1+m_1m_2} \right )  \right |$

Substituting the values of slopes

$\theta=\tan^{-1}\left | \left ( \frac{\frac{1}{\sqrt3}-\sqrt3}{1+\frac{1}{\sqrt3}\cdot\sqrt3} \right ) \right |\\\\\theta=\tan^{-1}\left | \left ( \frac{-2}{\sqrt3}\cdot\frac{1}{2} \right ) \right |\\\\\theta=\tan^{-1}\left ( \frac{1}{\sqrt3} \right )\\\\\theta=30^{\circ}$

Therefore, the acute angle between the lines is 30°

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Angle between the lines

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