Question

find acute angle between the pair of straight line in which the first value of y=(2-√3)x+4 and another value is y=(2+√3)x-7​

Answer 1

EXPLANATION.

→ pair of straight line in which the first value

of y = ( 2 - √3 )x + 4 and another value is

y = ( 2 + √3 )x - 7

→ slope of line → y = Mx + c

→ M¹ = ( 2 - √3)

→ M² = ( 2 + √3 )

$\sf : \implies \: \tan( \theta) = | \dfrac{ m_{1} - m_{2} }{1 + m_{1} m_{2} } | \\ \\ \sf : \implies \: \tan( \theta) = | \frac{(2 - \sqrt{3}) - (2 + \sqrt{3} )}{1 + (2 - \sqrt{3})(2 + \sqrt{3}) } | \\ \\ \sf : \implies \: \tan( \theta) \: = | \frac{2 - \sqrt{3} - 2 - \sqrt{3} }{1 + ( {2}^{2} - \sqrt{3} {}^{2} ) } | \\ \\ \sf : \implies \: \tan( \theta) \: = \: | \frac{ - 2 \sqrt{3} }{1 + (4 - 3)} | \\ \\ \sf : \implies \: \tan( \theta) \: = | \frac{ - 2 \sqrt{3} }{2} |$

$\sf : \implies \: \tan( \theta) = | - \sqrt{3} | \\ \\ \sf : \implies \: \tan( \theta) = \sqrt{3} \\ \\ \sf : \implies \: ( \theta) \: = 60 \degree$