Please help! If the diagonal of a parallelogram measures 40 cm, the angle opposite that diagonal is 50°11', and one side is 24 cm, find the other side of the parallelogram.

Question

jim_thompson5910 · Answer

A drawing may help

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jim_thompson5910 · Answer

Now you can use the law of cosines to solve for x

c^2 = a^2 + b^2 - 2ab*cos(C)

40^2 = 24^2 + x^2 - 2*24*x*cos(50 degrees 11 minutes)

Keep going to solve for x

anonymous · Answer

I tried that but you get a quadratic with messy numbers, how do you solve that?

jim_thompson5910 · Answer

what did you get

jim_thompson5910 · Answer

you would get a quadratic because of the x^2 and the x terms, so you can't avoid that

anonymous · Answer

0 = x^2 -48*cos(50°11')*x -1024

jim_thompson5910 · Answer

ok good, now you can evaluate the cosine of 50°11' to get some number

keep in mind

50°11' = 50 + 11/60

50°11' = 50 + 0.18333333333333

50°11' = 50.18333333333333 degrees

anonymous · Answer

So I guess I can simplify it to 0 = x^2 - 30.73599154 - 1024. But see, that's kind of messy (and I definitely can't factor that easily!)

jim_thompson5910 · Answer

If you can't factor, then use the quadratic formula

anonymous · Answer

Hmm okay.
x^2 - 30.73599154 - 1024  = 0
a = 1, b = -30.73599154 (for now I'll leave it as b), c = -1024
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That's not the answer :(