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In a Delta ABC, if tan.(A)/(2)=(5)/(6), ...

In a `Delta ABC`, if `tan.(A)/(2)=(5)/(6), tan.(B)/(2)=(20)/(37)`, then which of the following is/are correct ?

A

`angle B gt angle C`

B

`angle B lt angle C`

C

`a gt b gt c`

D

`a lt b lt c`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`tan.(A+B)/(2)=((5)/(6)+(20)/(37))/(1-(5)/(6).(20)/(37))=(305)/(122)`
`rArr tan.(C )/(2)=(122)/(305)`
`rArr tan.(B)/(2)gt tan.(C )/(2)`
`rArr angle B gt angle C`
Also `angle A gt angle B gt angle C`
Hence, `a gt b gt c`
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