In ` A B C ,a , ca n dA` are given and `b_1,b_2` are two values of the third side `b` such that `b_2=2b_1dot` Then prove that `sinA=sqrt((9a^2-c^2)/(8c^2))`

Explanation

`cosA=(b^2+c^2-a^2)/(2bc)`

`b^2-2bc*cosA+(c^2-a^2)=0`

`b_1+b_2=2cosA`

`b_1b_2=c^2-a^2`

`3b_1=2cosa,2b_1^2=c^2-a_2`

`2(2/3c cosA)^2=c^2-a^2`

`8c^2(1-sin^2A)=9c^2-9a^2`

`sinA=sqrt((9a^2-c^2)/(8c^2))`.