Answer:
about 41.9 square inches
Step-by-step explanation:
The area of a sector of radius r and central angle α is given by ...
A = (1/2)r^2·α
where α is in radians.
The angle 75° is equivalent to 75°·(π/180°) = 5π/12 radians, so the area is ...
A = (1/2)(8 in)^2·(5/12)·3.14 = (40/3)·3.14 in^2 = 41.86_6 in^2 ≈ 41.9 in^2
_____
Comment on the precision of the answer
The use of a 3-significant-digit value for pi means that the answer must be rounded to 3 significant digits. If the 8-inch value for radius is really only accurate to ±1/2 inch, then the answer must be rounded to 1 significant digit: 40 in^2.
