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.

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

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

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