The sides of a triangle are in the ratio `1: sqrt3:2.` Then the angles are in the ratio

Options

A. `1:3:5`
B. `2:3:4`
C. `3:2:1`
D. `1:2:3`

Answer

D

Explanation

Let in a `DeltaABC`,
`a:b:c=1:sqrt(3):2`
`:'a=k,b=ksqrt(3),c=2k`
where`kgt0`
`:.a^(2)+b^(2)=c^(2)`
`:.C=90^(@)`
`impliescoA=(b^(2)+c^(2)-a^(2))/(2bc)=(sqrt(3))/2`
`:.A=30^(@)`
`impliesB=180^(@)-(A+C)`
`=180^(@)-(30^(@)+90^(@))=60^(@)`
`:.A:B:C=30^(@):60^(@):90^(@)`
`=1:2:3`