Corollary 5.1b: The area of the isosceles triangle in the figure

is

c2sin(a)cos(a)

or

c2sin(b)cos(b)

 

proof 1: Half of the base is csin(a) or ccos(b). The height is ccos(a) or csin(b). In either event the area is either c2sin(a)cos(a) or c2sin(b)cos(b).

proof 2: By Theorem 5.1a, the area is c2sin(2a)/2. But sin(2a) = 2sin(a)cos(a). The other result follows from the fact that sin(b) = cos(a) and sin(a) = cos(b).

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