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The perimeter of a triangle ABC is six t...

The perimeter of a triangle ABC is six times the arithmetic mean of the sines of its angles. If the side a is 1, then find angle A

A

`pi/6`

B

`pi/3`

C

`pi/2`

D

`pi`

Text Solution

Verified by Experts

We have,
`a+b+c=(6(sinA+sinB+sinC))/3`
`rArrk(sin A+ sin B + sin C)= 2 (sin A+ sin B + sin C),`
where `k=a/(sinA)=b/(sinB)=c/(sinC)`
`rArrk=2` `[becausesinA+sinB+sinCne0]`
`rArra/(sinA)=2rArrsinA=1/2` `[because a=1]`
`rArrA=pi/6`
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