In a ` DeltaA B C ,` prove the following : The sides of a triangle area `a=5,\ b=6\ a n d\ c=8` , show that `8cosA+16 cos B+4c cos C=17.`

Explanation

We have, `a=4, b=6` and `c=8`

`cos A=frac{b^{2}+c^{2}-a^{2}}{2 b c}=frac{7}{8}`

`cos B=frac{a^{2}+c^{2}-b^{2}}{2 a c}=frac{11}{16}`

`cos C=frac{a^{2}+b^{2}-c^{2}}{2 a b}=frac{-1}{4}`

`8 cos A+16 cos B+4 cos C=8 times frac{7}{8}+16 times frac{11}{16}+4 times(-frac{1}{4}) `

=17