Answer:
8877.11 yd ^ 2
Step-by-step explanation:
What we must do to calculate the area of the triangle:
a = b * h / 2
b is the base and h is height.
To calculate the height we apply the following:
sin ° A = opposite / hypotenuse
the opposite side would come being the height, therefore:
height = sin ° A * hypotenuse
h = sin (38 °) * 516
h = 0.615 * 516
h = 317.67
And the base would be the other 503 value
therefore the area is:
a = 317.67 * 503/2
a = 79894 ft ^ 2
but we know that 1 ft ^ 2 is 0.111 and d ^ 2
Thus:
79894 ft ^ 2 * 0.111 = 8877.11 yd ^ 2
Answer:
Area = 8,877 yd2
Step-by-step explanation:
To find the area of the park, first we need to find the length of the third side.
To find it, we can use the law of cosines:
a^2 = b^2 + c^2 − 2*b*c*cos(A)
where a, b and c are sides of the triangle, and A is the vertix between the sides b and c.
So, with b = 503 and c = 516, we have that:
a^2 = 503^2 + 516^2 - 2*503*516*cos(38) = 110211.77
a = 331.98
Now we can use the Heron's formula to calculate the area of a scalene triangle (three different sides):
Area = sqrt[s*(s - a)*(s - b)*(s - c)]
where s is the half-perimeter of the triangle.
Calculating s, we have:
s = (a + b + c) / 2 = 675.49
Then, we find the area:
Area = sqrt[675.49*(675.49 - 331.98)*(675.49 - 503)*(675.49 - 516)] = 79896.52 ft2
Converting from square feet to square yards (1 ft2 = 1/9 yd2), we have:
Area = 79896.52/9 = 8877.39 yd2
