In a `Delta`ABC, a + b = 3 `(1 + sqrt(3))` cm and a - b = 3 `(1 - sqrt(3))` cm. If angle A is `30^(@)`, then what is the angle B ?

Options

A. `120^(@)`
B. `90^(@)`
C. `75^(@)`
D. `60^(@)`

Answer

D

Explanation

Given, `a + b = 3 (1 + sqrt(3))..........(1)`
and `a - b = 3(1- sqrt(3)).........(2)`
By adding (1) and (2) we get
`(a+b)+(a-b)=3+3sqrt(3)+3-3sqrt(3)`
`rArr 2a = 6 rArr a = 3`
`therefore b = 3 - 3 + 3sqrt(3) = 3 sqrt(3)`
By using sine rule, `rArr (a)/(sinA)=(b)/(sinB)`
Given `angle A = 30" "rArr (3)/(sin30^(@))=(3sqrt(3))/(sinB)`
`rArr sin B = sqrt(3)xx(1)/(2) rArr sin B = sin 60^(@)`
`rArr B = 60^(@)`