How do you use the law of cosines or law of sines if you are given a=11, b=7, c=9?

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How do you use the law of cosines or law of sines if you are given a=11, b=7, c=9?

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Answer 1 · 2015-06-16T22:35:12

Solve triangle by Law of cosines and sines

Explanation:

To find a triangle's angle use the Law of Cosines

$a^{2} = b^{2} + c^{2} - 2 b c . cos A$ $a^2 = b^2 + c^2 - 2bc.cos A$
$11^{2} = 7^{2} + 9^{2} - 2 (7) (9) cos A$ $11^2 = 7^2 + 9^2 - 2(7)(9)cos A$
$cos A = \frac{130 - 121}{126} = \frac{9}{126} = 0.07$ $cos A = (130 - 121)/126 = 9/126 = 0.07$ --> A = 85.90
$b^{2} = a^{2} + c^{2} - 2 a c . cos B$ $b^2 = a^2 + c^2 - 2ac.cos B$
49 = 121 + 81 - 198cos B
$cos B = \frac{153}{198} = 0.77$ $cos B = 153/198 = 0.77$ -> B = 39.40
Angle C = 180 - B - A = 180 - 39.40 - 85.90 = 54.70

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How do you use the law of cosines or law of sines if you are given a=11, b=7, c=9?

1 Answer

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