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The angles of a triangle are in the rati...

The angles of a triangle are in the ratio `1:2:3` , then the sides of a triangle are in the ratio

A

`1:sqrt(3):2`

B

`2:sqrt(3):1`

C

`sqrt(3):2:1`

D

`3:2:1`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `(angleA)/(1)=(angleB)/(2)=(angleC)/(3)=(A+B+C)/(1+2+3)=(180^(@))/(6)=30^(@)`
`thereforeangleA=30^(@),angleB=60^(@),angleC=90^(@)`
By sine rule ,
`a:b:c=sinA:sinB:sinC`
`=sin30^(@):sin60^(@):sin90^(@)`
`=(1)/(2):(sqrt(3))/(2):1=1:sqrt(3):2`
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