How do you use the law of cosines or law of sines if you are given length of b is 147, length of c is 216 and the angle A is 83,33°?

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Answer 1 · 2018-06-21T08:12:33

$color(violet)(hat B = 36.28^@, hat C = 60.39^@, b = 128.69$

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$b = 147, c = 216, hatA = 83.33^@, a = ?$

$a^2 = b^2 + c^2 - 2bc cosA$ as per law of cosines.

$a^2 = (147^2 + 216^2 - (2 * 147 * 216 * cos(83.33)) = 60888.966$

$a = sqrt(60888.966) = 246.76 " units"$

$a / sin A = c / sin C$

$sin C = (216 * sin (83.33)) / 246.76= 60.39^@$

$hat B = 180 - 83.33 - 60.39 = 36.28^@$

$b = ( 216 *sin(36.28) ) / sin (83.33) = 128.69$