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If the angles of the triangle are in A.P...

If the angles of the triangle are in A.P. and `3a^(2)=2b^(2)`, then angle C ,is

A

`(pi)/6`

B

`(pi)/3`

C

`pi/4`

D

`(5pi)/12`

Text Solution

Verified by Experts

It is given that A, B, Care in A.P.
`therefore2B=A+CrArr3B=A+B+C=pirArrB=pi/3`
Now,
`3a^(2)=2b^(2)`
`rArrb/a=sqrt(3/2)`
`rArr(sinB)/(sinA)=sqrt(3/2)`
`rArr(sinpi/3)/(sinA)=sqrt(3/2)rArrsinA=1/(sqrt2)rArrA=(pi)/4`
`thereforeC=pi-(pi/4+pi/3)=(5pi)/(12)`
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