Practice Test 10

A non-right triangle $\triangle DEF$ has $DE=5$, $DF=12$, and $EF=13$. The included angle at $D$ is emphasized.

Which reasoning correctly decides whether $\angle D$ is acute, right, or obtuse using the Law of Cosines as a generalization of the Pythagorean Theorem?

A non-right triangle $\triangle MNO$ has sides $MN=8$, $MO=13$, and $NO=17$. The included angle at $M$ is emphasized (between $MN$ and $MO$).

Which setup correctly finds $\angle M$ using a justification consistent with the Law of Cosines (as a Pythagorean generalization)?