What is the acute angle between the two straight lines y = ( ) 2– 3 x + 5 and y = ( ) 2 3 + x – 7 ? -Maths 9th

What is the acute angle between the two straight lines y = ( ) 2– 3 x + 5 and y = ( ) 2 3 + x – 7 ? -Maths 9th
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Answer :

(a) 60ºThe two lines are: y = \((2-\sqrt3)\) \(x\) + 5            ...(i) y = \((2-\sqrt3)\) \(x\) – 7               ...(ii) Slope of line (i), m1 = \(2-\sqrt3\)Slope of line (ii), m2 = \(2+\sqrt3\)If θ is the angle between the two lines, then tan θ = \(\big|rac{m_1-m_2}{1+m_1m_2}\big|\) = \(\bigg|rac{(2-\sqrt3)-(2+\sqrt3)}{1+(2-\sqrt3)(2+\sqrt3)}\bigg|\)= \(\bigg|rac{-2\sqrt3}{1+1}\bigg|=\sqrt3\)∴ θ = –1 tan ( 3) = 60º.
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