Answer:
Step-by-step explanation:
Let the center of the circle be O.
Recall that the area of a triangle can be given by:
Where <em>C</em> is the angle between the two sides.
ΔABP is equal to the sum of ΔAPO and ΔBOP.
Let <em>a</em> = OP and <em>b</em> = OB. Since this is the unit circle and PO and BO are radii, they both equal one. <em>C</em> will be θ. Hence, the area of ΔBOP is:
For ΔAPO, we can use the two sides OP and OA. Again, they are the radii of the unit circle, so they equal one. The angle in this case will be π - θ radians. Hence:
However, note that sin(π - θ) = sin(θ). Hence:
Hence, the area of ΔABP is: