In $triangle DEF, d=15, e=12, f=8$ , how do you find the cosine of each of the angles?

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Answer 1 · 2017-03-08T07:15:59

$cosD=-17/192, cosE=29/48, and, cosF=61/72.$

By the Cosine Rule, $cosD=(e^2+f^2-d^2)/(2ef)$

$:. cosD=(144+64-225)/{2(12)(8)}=-17/192.$

$cosE=(f^2+d^2-e^2)/(2fd)=(64+225-144)/{2(8)(15)}=145/{2(8)(15)}=29/48.$

$cosF=d^2+e^2-f^2/(2de)=(225+144-64)/{2(15)(12)}=305/{2(15)(12)}=61/72.$

In triangle DEF, d=15, e=12, f=8triangle DEF, d=15, e=12, f=8, how do you find the cosine of each of the angles?