How do you determine whether #triangle ABC# has no, one, or two solutions given #A=100^circ, a=7, b=3#?

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Answer 1 · 2018-02-19T06:36:27

One solution : #color(green)(a = 7, b = 3, c = 5.82#

#color(blue)(hatA = 100^@, hatB = 25^@, hatC = 55^@#

Given #hatA = 100^@, a = 7, b = 3#

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As per sine law, #a / sin A = b / sin B = c / sin C#

#sin B = (b * sin A ) / a = (3 * sin 100) / 7 = 0.4221#

#hatB = sin ^(-1) 0.4221 ~~ 25^@#

#hatC = 180 - 100 - 25 = 55^@#

#c = (a * sin C) / sin A = (7 * sin 55) / sin 100 ~~ 5.82#