How do you determine the number of possible solutions using the rule of law of sines given b=15.2, A=12°30', C=57°30'?

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How do you determine the number of possible solutions using the rule of law of sines given b=15.2, A=12°30', C=57°30'?

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Answer 1 · 2015-07-10T04:27:43

Solve triangle knowing b, A, and C

Explanation:

Find B, a and c.
Angle B = 180 - C - A = 180 - 57.30 - 12.30 = $110.40$ $110.40$ deg
Use trig identity: $\frac{a}{sin A} = \frac{b}{sin B}$ $a/sin A = b/sin B$

$a = b (\frac{sin B}{sin A}) = 15.2 (\frac{0.94}{0.21}) = 68.04$ $a = b(sin B/sin A) = 15.2(0.94/0.21) = 68.04$ ,

There are 2 possible solutions, because 0.94 is the same sin value of 2 angles: B = 110.40 and B = 69.60. However, the solution angle B = 69.60 is rejected, because the sum A + B + C must be 180 deg.

$c = b (\frac{sin B}{sin C}) = 15.2 (\frac{0.94}{0.84}) = 17.00$ $c = b(sin B/sin C) = 15.2(0.94/0.84) = 17.00$

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How do you determine the number of possible solutions using the rule of law of sines given b=15.2, A=12°30', C=57°30'?

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