First slide

Equation of line in Straight lines

Question

The acute angle between the lines $y = (2 - \sqrt{3}) (x - 6)$ and $y = (2 + \sqrt{3}) (x + 8)$ is

Moderate

A

$120 °$
B

$60 °$
C

$90 °$
D

$30 °$

Solution

If is acute angle between two lines $y = m_{1} (x - a)$ and $y = (2 + \sqrt{3}) (x + 8)$ then $\tan θ = |\frac{m_{1} - m_{2}}{1 + m_{1} m_{2}}|$
Hence,
$\begin{matrix} \tan θ = |\frac{(2 - \sqrt{3}) - (2 + \sqrt{3})}{1 + (2 - \sqrt{3}) (2 + \sqrt{3})}| \\ = |\frac{- 2 \sqrt{3}}{1 + 4 - 3}| \\ = \sqrt{3} \end{matrix}$
It gives
$θ = 60 °$
Therefore, the acute angle between the given lines is $θ = 60 °$

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