• # 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) $(2-\sqrt{3})x-y-4=0$

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.

You need to login to perform this action.
You will be redirected in 3 sec