Final answer:
The area of the triangular parcel of land can be calculated using Heron's formula. After finding the area in square yards, it can be converted to acres and multiplied by the cost per acre to find the total cost of the land.
Step-by-step explanation:
The area of a triangle can be calculated using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, and a, b, and c are the side lengths. In this case, the side lengths are 120 yards, 90 yards, and 102 yards. The semi-perimeter can be calculated using the formula:
s = (a + b + c) / 2
Plugging in the given values, we get:
s = (120 + 90 + 102) / 2 = 156
Using Heron's formula, the area of the triangle is:
A = √(156(156-120)(156-90)(156-102))
A ≈ 5841.78 square yards
To find the cost of the land, we need to convert the area from square yards to acres. There are 4840 square yards in one acre, so the land area is approximately 1.21 acres. Multiplying the area by the cost per acre, which is $3000, we get:
Cost = 1.21 acres * $3000/acre ≈ $3630
Therefore, the cost of the land is approximately $3630.