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Math Help - Equation of a line...

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    Equation of a line...

    The given figure represents the lines y = x +1 and y = 3 x -1. Write down the angles which the lines make with the positive direction of x-axis. Hence determine .
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    Quote Originally Posted by snigdha View Post
    The given figure represents the lines y = x +1 and y = 3 x -1. Write down the angles which the lines make with the positive direction of x-axis. Hence determine .
    Notice where the lines cross the x-axis.

    y=x+1 crosses at x=-1 and \sqrt{3}x-1 crosses at \frac{1}{\sqrt{3}}.

    Since the lines form a triangle with the x-axis, you can find the lenght of the side opposite of \theta using the x-intercepts.

    So just find the point where the lines intersect by solving x+1=\sqrt{3}x-1. Once you find the point, you should be able to find the lenghts of the sides.
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    The slopes of the lines are the coefficients of the 'x' term.

    What are the slopes of the hypotenuse of a 45,45,90 triangle? Of a 60,30,90 triangle?
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    Quote Originally Posted by snigdha View Post
    The given figure represents the lines y = x +1 and y = 3 x -1. Write down the angles which the lines make with the positive direction of x-axis. Hence determine .
    Hi snigdha,

    The line whose equation is y = x + 1 has a slope of 1.

    The acute angle formed with the positive direction of the x-axis (which is inside the triangle) is \tan^{-1}(1)={\color{red}45^{\circ}}

    The line whose equation is y=\sqrt{3}x-1 has a slope of \sqrt{3}.

    The acute angle formed with the positive direction of the x-axis is \tan^{-1}(\sqrt{3})=60^{\circ}.
    Now we're interested in the obtuse angle inside the triangle, so we determine the supplement of 60^{\circ} which is {\color{red}120^{\circ}}


    Now, you have two angles of the triangle and can determine the value of {\color{red}\Theta}
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