Question

Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is ${30}^{\circ }$.

Answer 1

Here p = 5 and $\alpha ={30}^{\circ }$

Putting these values in $xcos\alpha +ysin\alpha =p$, we have

$xcos{30}^{\circ }+ysin{30}^{\circ }=5$

$\Rightarrow \frac{\sqrt{3}}{2}x+\frac{1}{2}y=5\Rightarrow \sqrt{3}x+y=10$