Two of the three side lengths are given. To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle. Use the Law of Cosines for this task.
a^2 = b^2 + c^2 - 2ac*cosA
Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or
a^2 = 250000 + 572500 - 750000(-0.1736), or
= 692264
Then a = +sqrt(692264) = 832 yds
Use Heron's Formula to find the area of the land.
First, calculate s=(a+b+c)/2: (500+750+832)/2 = 1041=s
According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )
Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )
I will leave this calculation to you to complete.
Suppose the area of the land is A square yards. Convert this to acres, using the fact that 1 acre = 4840 yd^2.
In acres, the area is
1 acre
A* ---------------- = (A/4840) acres
4840 yd^2
How much will this cost? Recall that the unit cost of the land is $2300/acre.
Then the total cost will be:
$2300
(A/4840) acres * ------------- = 0.475*A dollars. (Substitute your value for A)
1 acre
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