If one side of a triangle is double the other, and the angles on opposite sides differ by `60^(@)`, then the triangle is

Options

A. equilateral
B. obtus angled
C. right angled
D. acute angled

Answer

C

Explanation

`a = 2b and A - B = 60^(@)`
We know that `tan.(A -B)/(2) = (a -b)/(a + b) cot.(C)/(2)`
or `tan 30^(@) = (1)/(3) cot.(C)/(2)`
or `tan.(C)/(2) = (1)/(sqrt3) " or " C = 60^(@)`
Hence, `A + B = 20^(@) " or " 2A = 180^(@)`
`rArr A = 90^(@), B = 30^(@), C = 60^(@)`