This additional side is equivalent to tangent of theta. Why? If we call this side say, Side C, tangent is defined as being the opposing side divided by the ajacent side, so tangent theta must be equal to Side C divided by the ajacent side, which in this case is just 1. Thus, Side C is equivalent to tangent of theta.
Notice that we can define three areas enclosed within these triangles:
This first blue area is equal to sin(theta)/2.
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