In `Delta`ABC, if `angle A : angle B : angle C = 1 : 2 : 3`, then what is BC : CA : AB ?

Options

A. `1 : 2 : 3`
B. `1 : sqrt(3) : 2`
C. `2 : sqrt(3) : 1`
D. `sqrt(3) : 1 : 2`

Answer

B

Explanation

Ratio of angles is given by `angle A : angle B : angle C = 1 : 2 : 3` Let `angle A = x, angle B = 2x and angle C = 3x`

We know that in a triangle `angle A + angle B + angle C = 180^(@)`
`rArr x + 2x + 3x = 180^(@)`
`rArr x=(180^(@))/(6)=30^(@)`
So, `angle A = 30^(@), angle B = 60^(@) and angle C = 90^(@)`
From sin law
`(BC)/(sinA)=(CA)/(sinB)=(AB)/(sinC)=K`
`(BC)/(sin30^(@))=(CA)/(sin60^(@))=(AB)/(sin90^(@))=K`
`BC = K sin 30^(@)`
`CA = K sin 60^(@)`
`AB = K sin 90^(@)`
BC : CA : AB
`= sin 30^(@) : sin 60^(@) : sin 90^(@) = (1)/(2) : (sqrt(3))/(2) : 1 : sqrt(3) : 2`