Question

Find the largest side of △XYZ, given that m∠Y=32°, m∠Z=67°, and m∠X=81°.

Answer 1

see below

Explanation:

According to the triangle larger angle theorem, if one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

So m∠X=81° is the largest angle in △XYZ, size YZ is opposite ∠X, then size YZ is the largest side.

According to law of sines, sin(A)/a = sin(B)/b = sin(C)/c

then we have: sin(81)/YZ = sin(32)/XY = sin(67)/XY

If we know the length of a side, you can calculate the other side based on law of sines.