Final answer:
The area of a triangle with sides a and b and included angle theta is given by the formula: Area = 1/2 * a * b * sin(theta)
Step-by-step explanation:
The area of a triangle with sides of length a and b and with included angle theta can be calculated using the formula:
Area = 1/2 * a * b * sin(theta)
This formula utilizes the sine function to calculate the area. It takes half of the product of the lengths of the two sides and the sine of the included angle.
For example, if a = 5 units, b = 7 units, and theta = 30 degrees, the area of the triangle would be:
Area = 1/2 * 5 * 7 * sin(30 degrees) = 8.75 square units