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.
A = 1/2bh
My answer is 139912.5.
Can someone help me with this please?
let base = 533'
height = 525' * sin(53º)
area = 1/2 * b * h = 1/2 * 533 * 525 * sin(53º)
To find the area of the park, you can use the formula for the area of a triangle, which is A = 1/2 * base * height (A = 1/2 * bh). However, we need to find the base and height of the triangle first.
Given that two adjacent sides of the park are 533 feet and 525 feet, we can label one side as the base (b) and the other as the height (h). The angle between these two sides is 53°.
To find the height (h) of the triangle, we can use trigonometry. In a right triangle, the sides adjacent to the angle can be found using cosine, which is adjacent/hypotenuse. In our case, the adjacent side is 525 feet and the hypotenuse is 533 feet.
cos(53°) = adjacent/hypotenuse
cos(53°) = 525/533
Now, solve for the adjacent side:
525 = cos(53°) * 533
Using a calculator, you can find that cos(53°) ≈ 0.6018.
Solving for the adjacent side:
525 ≈ 0.6018 * 533
525 ≈ 320.9166
Now, we have the base (b) ≈ 320.9166 feet and the height (h) ≈ 533 feet.
Next, we can calculate the area of the park using the formula A = 1/2 * bh.
A = 1/2 * 320.9166 * 533
A ≈ 85549.80
Rounding to the nearest square foot, the area of the park is approximately 85550 square feet.
To find the area of the triangular park, you can use the formula for the area of a triangle: A = 1/2 * base * height. However, in this case, we don't have the height of the triangle directly.
To find the height, we can use the trigonometric relationship between the angle and the sides of the triangle. In this case, we have two sides and the included angle.
To find the height (h), we can use the formula:
h = adjacent side * sin(angle)
Let's substitute the given values into the equation:
h = 525 ft * sin(53°)
To calculate sin(53°), you can use a scientific calculator or an online calculator. It is approximately 0.7986.
h = 525 ft * 0.7986 = 419.79 ft (rounding to two decimal places)
Now that we have the height (h) and the base (b), we can substitute these values into the formula for the area of a triangle:
A = 1/2 * 533 ft * 419.79 ft
Calculating this value gives us:
A = 111,852.885 ft²
Rounding this to the nearest square foot, we get an area of approximately 111,853 ft².
Therefore, the area of the park to the nearest square foot is approximately 111,853 ft².