question_answer

The equation of straight Sine which makes an angle of \[\mathbf{1}{{\mathbf{5}}^{{}^\circ }}\] with the positive direction of x-axis, cuts an intercept of the length 4 on the negative.

A) \[\left( 2-\sqrt{3} \right)x-y+4=0\]

B) \[(2-\sqrt{3})x+y-4=0\]

C) \[\left( 2-\sqrt{3} \right)x+y+4=0\]                 

D) \[(2-\sqrt{3})x-y-4=0\]

Correct Answer: D

Solution :

[d] Slope of the line, \[m=tan{{15}^{{}^\circ }}=tan\left( {{45}^{{}^\circ }}-{{30}^{{}^\circ }} \right)\] \[=\frac{\sqrt{3}-1}{\sqrt{3}+1\text{ }}=\frac{{{\left( \sqrt{3}-1 \right)}^{2}}}{\left( \sqrt{3}+1 \right)\left( \sqrt{3}-1 \right)\text{ }}=2-\sqrt{3}\] Here, \[c=-4\] Thus, the required equation of straight line be \[y=mx+c\] \[y=\left( 2-\sqrt{3} \right)x-4\] \[\left( 2-\sqrt{3} \right)x-y-4=0\] Hence, option [d] is correct.