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Let the angles A , Ba n dC of triangle A...

Let the angles `A , Ba n dC` of triangle `A B C` be in `AdotPdot` and let `b : c` be `sqrt(3):sqrt(2)` . Find angle `Adot`

A

`75^(@)`

B

`60^(@)`

C

`45^(@)`

D

`30^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`2B=A+CimpliesB=60^(@)" "[because A+B+C=180^(@)]`
Now,
`b:c=sqrt(3):sqrt(2)`
`impliessinB:sinC=sqrt(3):sqrt(2)`
`implies (sinB)/(sqrt(3))=(sinC)/(sqrt(2))implies(sin60^(@))/(sqrt(3))=(sinC)/(sqrt(2))`
`implies sinC=(1)/(sqrt(2))impliesC=45^(@)`
`therefore A+B+C=180^(@)impliesA=75^(@)`
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