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A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53°. Find the area of the park to the nearest square foot.
(3 points)
To find the area of the park, we can use the formula for the area of a triangle: Area = (1/2) * base * height.
First, we need to find the height of the triangle. We can use trigonometry to find the height, since we have the angle and one side length.
Using the sine function, we can write: sin(53°) = height / 525 feet.
Rearranging the equation to solve for height, we have: height = sin(53°) * 525 feet.
Using a calculator, we can find that sin(53°) ≈ 0.7986.
Substituting the values, we have: height = 0.7986 * 525 feet ≈ 419.286 feet.
Now, we can calculate the area of the park using the formula mentioned earlier.
Area = (1/2) * 533 feet * 419.286 feet.
Area ≈ (1/2) * 533 feet * 419.286 feet ≈ 111,526.498 square feet.
Therefore, the area of the park is approximately 111,526 square feet.