Question 67447: The legnths of two adjacent sides of a parallelogram are 6 and 15. If the measure of an included angle is 60 degrees. What is the legnth of the shorter diagnol of the parallelogram?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The lengths of two adjacent sides of a parallelogram are 6 and 15. If the measure of an included angle is 60 degrees. What is the length of the shorter diagonal of the parallelogram?
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We know the short diagonal is opposite the smaller angle, in this case it's 60 deg
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Draw the triangle, Let A = 60 degrees, the diagonal = a, b = 15, c = 6
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We have side-angle-side here which lends itself to the law of cosines:
a^2 = b^2 + c^2 - 2(b*c)cos(A)
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a^2 = 15^2 + 6^2 - 2(15*6)Cos(60)
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a^2 = 225 + 36 - 2(90)(.5)
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a^2 = 261 - 90
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a = SqRt(171)
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a = 13.1 is the length of the shorter diagonal
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