The acute angle between the lines x cos 30^{c | vedclass

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(B) The given equations of the lines are $x \cos 30^{\circ} + y \sin 30^{\circ} = 3$ and $x \cos 60^{\circ} + y \sin 60^{\circ} = 5$. These are in the

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$30$

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(B) The given equations of the lines are $x \cos 30^{\circ} + y \sin 30^{\circ} = 3$ and $x \cos 60^{\circ} + y \sin 60^{\circ} = 5$. These are in the normal form $x \cos \alpha + y \sin \alpha = p$,where $\alpha$ is the angle made by the normal to the line with the positive $x$-axis. The angle of the normal to the first line is $\alpha_1 = 30^{\circ}$ and to the second line is $\alpha_2 = 60^{\circ}$. The angle $	heta$ between two lines is equal to the angle between their normals. Therefore,$	heta = |\alpha_2 - \alpha_1| = |60^{\circ} - 30^{\circ}| = 30^{\circ}$.

The acute angle between the lines $x \cos 30^{\circ} + y \sin 30^{\circ} = 3$ and $x \cos 60^{\circ} + y \sin 60^{\circ} = 5$ is (in $^{\circ}$)

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