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There exists a triangle A B C satisfying...

There exists a triangle `A B C` satisfying the conditions `bsinA=a ,A a ,A >pi/2` `bsinA > a ,A>a` `bsinA<>pi/2,b=a`

A

`bsin A=a,Alt(pi)/(2)`

B

`bsin Agta,Agt(pi)/(2)`

C

`bsin Agta,Alt(pi)/(2)`

D

`bsin Alta,Alt(pi)/(2),bgta`

Text Solution

Verified by Experts

The correct Answer is:
A, D
The sine formula is
`(a)/(sinA)=(b)/(sin B) rArr sin B=b sin A`
(a) `b sin A= a rAr a sin B=a`
`rArr B=(pi)/(2)`
Since, `angle Alt(pi)/(2)`, therefore the triangle is possible.
(b) and (c) b sin `Agta`
`rArr a sin B a rAr sin Bgt1`
(d) `b sin A lta`
`rArr a sin B lt a rArr sin B lt rArr angleB` exists.
Now, `bgta rArr BgtA`
Since `Alt(pi)/(2)`
`:.` The triangle is possible.
Hence, (a) and (d) are the correct answers.
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