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In a triangle ABC,if B=30^@ " and " c = ...

In a triangle ABC,if B=`30^@ " and " c = sqrt(3)` b the A can be equal to

A

`45^@`

B

`60^@`

C

`90^@`

D

`120^@`

Text Solution

Verified by Experts

We have cos `B =(c^2+a^2-b^2)/(2ca) rArr (sqrt3)/(2)=(3b^2+a^2-b^2)/(2xx sqrt(3b)xxa)`
`rArr a^2-3ab+2ab^2=0 rArr (a-2b)(a-b)=0`
`rArr "Either a " = b rArr A = 30 ^@`
or a= 2b `rArr a^2=4b^2=b^2+c^2rArr A = 90 ^@`
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