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)

Answer 1

To find the area of the triangular park, we can use the formula for the area of a triangle:

Area = 0.5 * base * height

First, we need to find the height of the triangle. We can split the triangle into two right triangles by drawing a perpendicular line from the vertex opposite the 525 feet side to create a right angle.

Using trigonometry, we can find the height:

sin(53°) = height / 533 feet
height = 533 feet * sin(53°)
height ≈ 437.64 feet

Now we can find the area of the triangle:

Area = 0.5 * 525 feet * 437.64 feet
Area ≈ 114,735 square feet

Therefore, the area of the park is approximately 114,735 square feet.