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The side of a triangle are in the ratio ...

The side of a triangle are in the ratio `1 : sqrt3:2`, then the angles of the triangle are the ratio

A

`1:3:5`

B

`2:3:2`

C

`3:2:1`

D

`1:2:3`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `a:b:c=1"sqrt(3):2rArrc^(2)=a^(2)+b^(2)`
`:.` Triangle is right angled at C

or `angleC=90^(@)`
and `(a)/(b)=(1)/(sqrt(3))`
In `DeltaBAC, tan A=(a)/(b)=(1)/(sqrt(3))`
`rArr A=30^(@)`
and `B=60^(@)" "[ :. A+B=90^(@)]`
`:.` Ratio of angles. `A:B:C=30^(@)60^(@):90^(@)=1:2:3`
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