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

Sides are in the ratio `1 : sqrt3 : 2`
Let `a = k, b = sqrt3 k, and c = 2k`
`cosA = (b^(2) + c^(2) - a^(2))/(2bc) = (sqrt3)/(2) rArr A = (pi)/(6)`
`cos B = (c^(2) + a^(2) -b^(2))/(2ac) = (1)/(2) rArr B = (pi)/(3)`
`rArr C = pi - bar(A + B) = (pi)/(2)`
`rArr A: B: C = 1 : 2: 3`