Given the area of 95 square feet and side AC of 13 feet, the value of side b, opposite the 65° angle, is 7 feet rounded to the nearest foot. Thus, the correct option is A.
From the image, we see that triangle ABC is a right triangle with a right angle at C. We are given that the area of the triangle is 95 square feet and that the length of side AC is 13 feet. We want to find the length of side b, which is opposite the 65° angle.
To find the area of a right triangle, we use the formula:
Area = (1/2) * base * height
In this case, the base is side b and the height is side AC. We are given that the area is 95 square feet and that AC is 13 feet, so we can plug these values into the formula to solve for b:
95 = (1/2) * b * 13
b = 95 * 2 / 13
b = 7.3 feet
Since we are asked to round the answer to the nearest foot, we round 7.3 feet up to 7 feet.
Therefore, the value of b, to the nearest foot, is 7 ft.