1 Answer

IrishGringo · Answer 1 · 2019-04-11T09:00:07+0000

Since you have the 42-deg angle and the length of the opposite side, 31, you can use the Law of Sines.

$(a)/(\sin A) = (b)/(\sin B) = (c)/(\sin C)$

We will use the law of sines first to find x.

Once we know x, we can find the angle opposite y.

Then we can find y.

$(31)/(\sin 42^\circ) = (37)/(\sin x)$

$\sin x = (37\sin 42^\circ)/(31)$

$\sin x = 0.798639$

$x = \sin^(-1) 0.798639 = 53^\circ$

Let z = the angle opposite y.

z + 42 + 53 = 180

z = 85

$(31)/(\sin 42^\circ) = (y)/(\sin 85^\circ)$

$y = (31 \sin 85^\circ)/(\sin 42^\circ)$

y = 46.2

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