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

Question

MN≈

m∠PNM≈ °, m∠ PM N≈ °

Answer 1

law of cosines is the equation

c^2 = a^2 + b^2 -2ab(cosC) where C is the angle opposite side c

MN^2 = 25^2 + 38.2^2 - 2(25)(38.2)cos23, solve for MN, then plug it into the next 2 equations to solve for the two angles PNM and PMN

25^2=38.2^2 + MN^2 - 2(38.2)(MN)cosPNM

38.2^2 = 25^2 + MN^2 -2(25)(MN)cosPMN