Question

A park in a subdivision is triangular shaped. Two adjacent sides of the park are 503 feet and 516 feet. The angle between the sides is 38 degrees. To the nearest unit, what is the area of the park in square yards? 17,755 26,632 8,877 11,363

Answer 1

Area = 8,877 yd2

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

Answer 2

8877.11 yd ^ 2

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