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Math Help - Length of Shorter Diagonal

  1. #1
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    Length of Shorter Diagonal

    The lengths of two adjacent sides of a parallelogram are 6 and 15. If the degree measure of the included angle is 60, what is the length of the shorter diagonal of the parallelogram?

    (a) sqrt{171}

    (b) sqrt{148}

    (c) sqrt{153}

    (d) sqrt{261}
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  2. #2
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    Quote Originally Posted by sharkman View Post
    The lengths of two adjacent sides of a parallelogram are 6 and 15. If the degree measure of the included angle is 60, what is the length of the shorter diagonal of the parallelogram?

    (a) sqrt{171}

    (b) sqrt{148}

    (c) sqrt{153}

    (d) sqrt{261}
    make a sketch and use the law of cosines ...

    a=\sqrt{b^2+c^2-2bc\cos{A}}
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    thanks but...

    Quote Originally Posted by skeeter View Post
    make a sketch and use the law of cosines ...

    a=\sqrt{b^2+c^2-2bc\cos{A}}
    Thank you but this question comes from a chapter on special right triangles. There is no mention of trig in that chapter at all.
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    Quote Originally Posted by sharkman View Post
    Thank you but this question comes from a chapter on special right triangles. There is no mention of trig in that chapter at all.
    draw in the altitude from the end of the side of length 6 perpendicular to the side of length 15 ... a 30-60-90 triangle is formed with hypotenuse length 6.

    determine the length of the altitude, a using the known side ratios of a 30-60-90 triangle.

    another right triangle is formed with legs of length " a" and b = 12.

    the hypotenuse of that right triangle is the short diagonal ... use Pythagoras to find its length.


    next time, please be sure to include all information about a problem, especially what methods can be used to solve it.
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    yes...

    Quote Originally Posted by skeeter View Post
    draw in the altitude from the end of the side of length 6 perpendicular to the side of length 15 ... a 30-60-90 triangle is formed with hypotenuse length 6.

    determine the length of the altitude, a using the known side ratios of a 30-60-90 triangle.

    another right triangle is formed with legs of length " a" and b = 12.

    the hypotenuse of that right triangle is the short diagonal ... use Pythagoras to find its length.


    next time, please be sure to include all information about a problem, especially what methods can be used to solve it.
    Exactly what I needed.
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