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)`
B. `2(sqrt(3)+1)`
C. `(sqrt(3)+1)/(3)`
D. `(sqrt(3)-1)/(2)`

Answer

A

Explanation

From `Delta ADB, AD = BD = x` In `Delta ADC`,
`tan30^(@)=(x)/(sqrt(3)+1-x)`
`rArr (1)/(sqrt(3))=(x)/(sqrt(3)+1-x)rArr sqrt(3)x=sqrt(3)+1-x`
`rArr (sqrt(3)+1)x = sqrt(3)+1`
`x=(sqrt(3)+1)/(sqrt(3)+1)=1`.
Area of `Delta`ABC = `(1)/(2)xx(sqrt(3)+1)xx1=(sqrt(3)+1)/(2)`