#color(blue)("Assumption: ")#
As # pi # is used in the angular measure it is assumed that the unit is radians. (Not stated)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Method Plane")#
Determine #/_cba#
Using Sine Rule and #/_cba# determine length of side A
Determine h using #h=Asin((5pi)/12)#
Determine area #hxxB/2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine" /_cba)#
Sum internal angles of a triangle is #180^0 = pi" radians"#
#=>/_cba= pi-(5pi)/12-pi/12#
#color(brown)(/_cba = pi/2 -> 90^o)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine length of A")#
Using #B/(sin(b))=A/sin(a)#
#=> 3/(sin(pi/2)) =A/sin(pi/12)#
#=> A= (3xxsin(pi/12))/(sin(pi/2))#
But #sin(pi/2) = 1#
#color(blue)(=> A = 3xxsin(pi/12))#
#color(brown)("This is an exact value so keep it in this form for now to reduce error")# #color(brown)("on final calculation.")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine h")#
#h=Asin((5pi)/12)#
#=>h=3xxsin(pi/12)xxsin((5pi)/12)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To determine area")#
#"area "= B/2xxh#
#"area "= 3/2 xx3xx sin(pi/12)xxsin((5pi)/12)#
but #sin(pi/12)xxsin((5pi)/12)=1/4#
#"area "= 3/2 xx3xx1/4#
#color(green)("area " = 1.125 " units"^2 -> 1 1/8 " units"^2)#
