use the trigonometry area formula to find the area to th nearest inch of △ABC, given a=7 inches, b=12 inches, and ∠C=77 degrees.
To find the area of △ABC using trigonometry, we can use the formula:
Area = (1/2) * a * b * sin(C)
Given that a = 7 inches, b = 12 inches, and ∠C = 77 degrees, we can substitute these values into the formula to find the area.
Area = (1/2) * 7 * 12 * sin(77 degrees)
Using a calculator, we find that sin(77 degrees) ≈ 0.9755.
Area = (1/2) * 7 * 12 * 0.9755
Area ≈ 42.98 square inches
Rounded to the nearest inch, the area of △ABC is approximately 43 square inches.