To maximize the area of a triangle formed by two sides of lengths a and b, with the angle between these sides being θ, we can use the formula for the area of a triangle:
Area = (1/2) * a * b * sin(θ)
In this equation, the area is dependent on the sine of the angle θ. The sine function reaches its maximum value of 1 when the angle is 90 degrees. Therefore, to maximize the area of the triangle, the angle θ should be set to 90 degrees.
Thus, when θ = 90, the triangle attains its maximum possible area, given the sides a and b.