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A triangle has vertices​ A(0,0)A(0,0), B(1,0)B(1,0), and​ CC, where CC is the point on the unit circle corresponding to an​ angle, XX, of 105∘105^\circ when it is drawn in standard position. Find the area of the triangle.

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Q. A triangle has vertices​ A(0,0)A(0,0), B(1,0)B(1,0), and​ CC, where CC is the point on the unit circle corresponding to an​ angle, XX, of 105∘105^\circ when it is drawn in standard position. Find the area of the triangle.
  1. Calculate Point C Coordinates: Calculate the coordinates of point C on the unit circle for an angle of 105105 degrees. Use the formulas x=cos⁡(θ)x = \cos(\theta) and y=sin⁡(θ)y = \sin(\theta) where θ\theta is in radians.
  2. Use Triangle Area Formula: Use the formula for the area of a triangle with vertices at (x1,y1)(x_1, y_1), (x2,y2)(x_2, y_2), and (x3,y3)(x_3, y_3): Area=0.5×∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣.\text{Area} = 0.5 \times |x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)|.
  3. Calculate Final Area: Calculate the final area.

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