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In a DeltaABC ,a =5 , b= 4 , and tanC/2=...

In a `DeltaABC` ,a =5 , b= 4 , and `tanC/2=sqrt(7/9)`, then c =

A

6

B

3

C

2

D

none of these

Text Solution

Verified by Experts

We have,
`tanC/2=sqrt(7/9)`
`rArr((s-a)(s-b))/(s(s-c)=7/9`
`rArr((2s-2a)(2s-2b))/(2s(2s-2c))=7/9`
`rArr((c-1)(c+1))/(9+c)(9-c)=7/9rArr(c^(2)-1)/(81-c^(2)=7/9rArrc=6`
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