Question

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

Answer 1

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

Explanation:

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.`