Question

abby used the law of cosines for △kmn to solve for k. ( k^2 = 31^2 + 53^2 - 2(31)(53)cos(37^circ) )
what additional information did abby know that is not shown in the diagram?
( mangle k = 37^circ ) and ( n = 31 )
( mangle k = 37^circ ) and ( k = 31 )
( mangle n = 37^circ ) and ( n = 31 )
( mangle n = 37^circ ) and ( k = 31 )
law of cosines: ( a^2 = b^2 + c^2 - 2bccos(a) )

Explanation:

The law of cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\). In the given equation \(k^{2}=31^{2}+53^{2}-2(31)(53)\cos(37^{\circ})\), by comparing with the formula, we can see that \(A = \angle K\) (the angle opposite side \(k\)), \(b = 31\) (side \(n\)), and \(c = 53\).

Answer:

\(m\angle K = 37^{\circ}\) and \(n = 31\)