The campground at a park is designed in a triangular fashion, surrounded on all three sides by trails. The property has 3535 feet of frontage on one trail, and 3333 feet of frontage on another; these two trails intersect at a 47°47° angle. What is the square footage of the attraction? Round to the nearest hundredth.
Question
The campground at a park is designed in a triangular fashion, surrounded on all three sides by trails. The property has 3535 feet of frontage on one trail, and 3333 feet of frontage on another; these two trails intersect at a 47°47° angle. What is the square footage of the attraction? Round to the nearest hundredth.
Solution
To find the area of a triangle given two sides and the included angle, you can use the formula:
Area = 1/2 * a * b * sin(C)
where a and b are the lengths of the two sides, and C is the included angle.
In this case, a = 3535 feet, b = 3333 feet, and C = 47 degrees.
First, convert the angle from degrees to radians because the sine function in most calculators uses radians. To convert from degrees to radians, multiply by π/180. So, C = 47 * π/180 = 0.8203 radians.
Then, substitute these values into the formula:
Area = 1/2 * 3535 * 3333 * sin(0.8203) = 4,872,411.77 square feet.
So, the square footage of the attraction is approximately 4,872,411.77 square feet, rounded to the nearest hundredth.
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