Given `b = 2, c = sqrt3, angle A = 30^(@)`, then inradius of `DeltaABC` is

Options

A. `(sqrt3 -1)/(2)`
B. `(sqrt3 + 1)/(2)`
C. `(sqrt3-1)/(4)`
D. none of these

Answer

A

Explanation

`b = 2, c = sqrt3, anlge A = 30^(@)`
`a = sqrt(b^(2) + c^(2) - 2bc cos A)`
`= sqrt(4+3 - 2 xx 2 sqrt3 (sqrt3)/(2)) = 1`
`rArr r = (s-a) tan.(A)/(2)`
`= (b + c-a)/(2) tan.(A)/(2)`
`= (sqrt3 +1)/(2) tan 15^(@)`
`= (sqrt3 +1)/(2) (sqrt3 -1)/(sqrt3+1) = (sqrt3 -1)/(2)`