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A parallelogram has sides measuring 7 and 9. Its shorter diagonal has a length of 8.  Find the measure of the longer diagonal.

 Jan 5, 2021
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using law of cosines
8^2 = 7^2+9^2 - 2*7*9 cos A
64 = 49 + 81 - 126 cos A
cos A = 66/126

x^2 = 130 - 126 cos(180-A)
but cos(180-A) = -cos A
so
x^2 = 130 + 126(66/126)
x^2 = 196
x = 14

 Jan 5, 2021

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