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In a triangle angleA=55^(@),angleB=15^(@...

In a triangle `angleA=55^(@),angleB=15^(@),angleC=110^(@)`. Then `c^(2)-a^(2)` is equal to

A

ab

B

2ab

C

`-ab`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(c )/(sin 110^(@))=(b)/(sin 15^(@))=(a)/(sin 55^(@))=k`
Now `c^(2)-a^(2)`
`=k^(2)sin^(2)110^(@)-k^(2)sin^(2)55^(@)`
`k^(2)sin 165^(@)sin 55^(@)`
`=(k sin 55^(@))(k sin 15^(@))`
= ab
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