1.

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))`

Answer» `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))`.


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