Final answer:
To find the area of ΔABC, use the formula A = 1/2 * base * height. The area of ΔABC is approximately 489 square feet.
Step-by-step explanation:
To find the area of the triangle ABC, we can use the formula A = 1/2 * base * height. The base of the triangle is side a, which has a length of 25 feet, and the height can be found using the sine function. Since we know the angle at vertex B is 83°, we can use the formula height = side c * sin(angle). So, the area of ΔABC is A = 1/2 * 25 feet * 40 feet * sin(83°).
Plugging in the values, A = 1/2 * 25 ft * 40 ft * sin(83°) = 500 ft² * sin(83°). Using a calculator, we find that sin(83°) ≈ 0.978. Therefore, the area of ΔABC is approximately 500 ft² * 0.978 ≈ 489. The area of ΔABC is approximately 489 square feet.