If the angles of a triangle are `30^0a n d45^0` and the included side is `(sqrt(3)+1)c m` then the area of the triangle is______.

Options

A. `(sqrt(3)-1)/(2)cm^(2)`
B. `(sqrt(3)+1)/(2)cm^(2)`
C. `(sqrt(3)-1)cm^(2)`
D. none of these

Answer

B

Explanation

Let ABC be the triangle in which `a=sqrt(3)+1` cm, `angleB=30^(@) and angleC=45^(@)."Then "angleC=180^(@)-angleA-angleB=105^(@)`.
`therefore b=(asinB)/(sinA) and c=(asinC)/(sinA)`
`implies b=((sqrt(3)+1)sin30^(@))/(sin 105^(@)) and c=((sqrt(3)+1)sin45^(@))/(sin105^(@))`
`implies b = sqrt(2) and c = 2`
`therefore " Area of "DeltaABC = (1)/(2) bc sin A = (sqrt(3)+1)/(2)cm^(2)`