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In a DeltaABC if the length of the sides...

In a `DeltaABC` if the length of the sides are `sqrt(2), sqrt(6)` and `sqrt(8)`, then the measures of the angles are

A

`30^(@), 60^(@), 90^(@)`

B

`45^(@), 75^(@), 60^(@)`

C

`45^(@), 30^(@), 105^(@)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `a=sqrt(2),b=sqrt(6)andc=sqrt(8)`. Then,
`cosA=(b^(2)+c^(2)-a^(2))/(2bc)impliescosA=(6+8-2)/(2sqrt(48))=sqrt(3)/(2)impliesA=30^(@)`
`cosB =(c^(2)+a^(2)-b^(2))/(2ac)impliescosB=(8+2-6)/(2sqrt(16))=(1)/(2)impliesB=60^(@)`
`therefore c=180^(@)-(A+B)=90^(@)`
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