How do you determine whether #triangle ABC# has no, one, or two solutions given #A=30^circ, a=17, b=34#?

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Answer 1 · 2018-02-18T10:44:22

It has one solution.

#a = 17, b = 34, c = 17sqrt3, hatA = 30^@, hatB = 90^@, hat C = 60^@#

#a / sin A = b / sin B = c / sin C#

Given #hat A = 30^@, a = 17, b = 34#

#sin B = (34 * sin 30)/17 = 1#

#hatB = sin^(-1) 1 = 90^@# It’s a right triangle.

#hatC = 180 - 30 - 90 = 60^@#

#c = (sin C * 34)/1 = 29.4449#