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

Question

6939 views around the world

You can reuse this answer
Creative Commons License

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:

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

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

$c ~~28.0$