Solve the triangles with the given parts using Law of Cosines:

Question

Solve the triangles with the given parts using Law of Cosines:

m∠Z = ?°, m∠X =? °, XZ =?

Answer 1

XZ² = 103² + 68² - 2(103)(68)cos33°

Once you have XZ, you might switch to law of sines to get angle Z. (Note: Z is the smaller of the 2 remaining angles, so you won’t have to worry about the L o S giving an acute angle when the angle is actually obtuse — sin^-1 never outputs an obtuse angle, even when the angle being solved for is obtuse.)

It is also possible to use L o C to get a 2nd angle.

It is always easiest to use the sum of interior angles = 180° to find the 3rd angle.