The equations y = pm sqrt{3}x and y = 1 repre | vedclass

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(A) The given equations are $y = \sqrt{3}x$,$y = -\sqrt{3}x$,and $y = 1$.These can be written as $y = 	an(60^{\circ})x$,$y = 	an(120^{\circ})x$,and

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an equilateral triangle

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(A) The given equations are $y = \sqrt{3}x$,$y = -\sqrt{3}x$,and $y = 1$.These can be written as $y = 	an(60^{\circ})x$,$y = 	an(120^{\circ})x$,and $y = 1$.The lines $y = \sqrt{3}x$ and $y = -\sqrt{3}x$ pass through the origin $(0,0)$ and make angles of $60^{\circ}$ and $120^{\circ}$ with the positive $x$-axis,respectively.The angle between these two lines is $120^{\circ} - 60^{\circ} = 60^{\circ}$.The line $y = 1$ intersects $y = \sqrt{3}x$ at $(\frac{1}{\sqrt{3}}, 1)$ and $y = -\sqrt{3}x$ at $(-\frac{1}{\sqrt{3}}, 1)$.The length of the base on the line $y = 1$ is $\frac{1}{\sqrt{3}} - (-\frac{1}{\sqrt{3}}) = \frac{2}{\sqrt{3}}$.The lengths of the other two sides are $\sqrt{(\frac{1}{\sqrt{3}})^2 + 1^2} = \sqrt{\frac{1}{3} + 1} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$.Since all three sides are equal to $\frac{2}{\sqrt{3}}$,the triangle is an equilateral triangle.

The equations $y = \pm \sqrt{3}x$ and $y = 1$ represent the sides of which triangle?

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