We can use the formula for the area of a triangle:
Area = (1/2) * base * height
where the base and height of the triangle can be any two sides of the triangle, as long as they form a right angle.
In this case, we are given the lengths of sides a and b, but we do not have the height of the triangle. However, we can use the law of sines to find the height:
sin(C) / c = sin(A) / a
sin(100°) / c = sin(A) / 12
Solving for sin(A), we get:
sin(A) = (12 * sin(100°)) / c
sin(A) = (12 * sin(100°)) / 17 (since c = b = 17)
sin(A) ≈ 0.7049
Now, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
where base = a = 12 and height = b * sin(A) = 17 * sin(A):
Area = (1/2) * 12 * 17 * sin(A)
Area ≈ 103.5
Therefore, the area of triangle ABC is approximately 103.5 square units.