Final answer:
Using the formula ½ * b * c * sin(A), with b=21, c=15, and a 72° angle, the area of the triangle is calculated to be 157.498 square units, rounded to 157.500 as per the question's request.
Step-by-step explanation:
To find the area of a triangle given the lengths of two sides and the measure of the included angle, we use the formula derived from the law of cosines:
Area = ½ * b * c * sin(A)
Given b=21, c=15, and m∠A=72°:
Area = ½ * 21 * 15 * sin(72°)
Convert the angle from degrees to radians if necessary (it's not in this case, as most calculators have a degree mode), and then calculate the sine:
Area = ½ * 21 * 15 * 0.9511 (assuming sin(72°) approximately equals 0.9511)
Area = 157.49775
After rounding to three decimal places, the area of the triangle is 157.498 square units, which can also be written as 157.500 to adhere to the question format. Therefore, the correct answer is a) 157.500.