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December 10th, 2009, 12:10 PM   #1
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How can solve this simple equation please step by step

-A cos 30° + B cos 45° =0
A sin 30° + B sin 45° =147
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December 10th, 2009, 01:15 PM   #2
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Re: How can solve this simple equation please step by step

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Originally Posted by falcon
-A cos 30° + B cos 45° =0
A sin 30° + B sin 45° =147
Plug in the specific values for the cos and sin of the given angles. (sin30° = 1/2 cos30° = ?(3)/2, sin 45°=cos45° = ?(2)/2) and solve linear equations. This is especially easy because sin45°=cos45°, so you have A(sin30° + cos30°) = 147. You should be able to finish.
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December 10th, 2009, 01:20 PM   #3
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Since cos 45° = sin 45°, subtracting the first equation from the second gives A(sin 30° + cos 30°) = 147.
Hence A = 147/(sin 30° + cos 30°)
             = 147(cos 30° - sin 30°)/(cos²30° - sin²30°)
             = 147(cos 30° - sin 30°)/cos 60°
             = 147((?3)/2 - 1/2)/(1/2)
             = 147?3 - 147.

From the first equation, B = A cos 30° / cos 45° = (147?3 - 147)((?3)/2)/(1/?2) = (441?2 - 147?6)/2.
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December 11th, 2009, 03:44 PM   #4
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Re: How can solve this simple equation please step by step

thanks for help
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