# Pre-Calculus

A parallelogram has adjacent sides 7 cm and 15 cm. If the shorter diagonal is 10 cm long, find the length of the longer diagonal.

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1. using the law of cosines, we know that

7^2+15^2-2*7*15 cosθ = 10^2
cosθ = (7^2+15^2-10^2)/(2*7*15) = 29/35

So, that means the other diagonal, x is

x^2 = 7^2+15^2+2*7*15*29/35 = 448
x = 8√7

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2. A parallelogram has adjacent sides 8 cm and 13cm. If the shorter diagonal is 11 cm long, find the length of the longer diagonal.

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