How do you solve the triangle given m∠B = 117°, a = 16, b = 38?

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Answer 1 · 2016-10-25T16:34:42

Please see the explanation for the process of "How to".

Using the Law of Sines , we can find the measure of #/_A#

#/_A = sin^-1((a/b)sin(/_B))#

#/_A = sin^-1((16/38)sin(117^@))#

#/_A ~~ 22^@#

To find the measure of #/_C#, use the fact that the sum of the angles of a triangle is 180°.

#/_C = 180^@ - 117^@ - 22^@#

#/_C = 41^@#

Use the Law of Sines to find the length of side c:

#c = asin(/_C)/sin(/_A)#

#c = 16sin(41^@)/sin(22^@)#

#c ~~28.0#