If in triangle the angles be to the one another as `1:2:3` , prove that the corresponding sides are `1:sqrt(3): 2.`

Options

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

Answer

C

Explanation

Given, angles of triangle are in ratio 1 : 2 : 3 Consider, `A=30^(@), B=60^(@) and C = 90^(@)`
We know, `(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`
`rArr (a)/(sin30^(@))=(b)/(sin60^(@))=(c)/(sin90^(@))`
`rArr (a)/((1)/(2))=(b)/((sqrt(3))/(2))=(c)/(1)`
`rArr a : b : c = (1)/(2) : (sqrt(3))/(2) : 1 = 1 : sqrt(3) : 2`