We have a triangle ABC where AB=c, BC=a, and CA=b
AB=827 ft, BC=110 ft, and CA=820 ft
so c=827, a=110, and b=820
using the law of cosines we have a^2=b^2+c^2-2bc cos(A)
angle A is opposite BC, angle B is opposite AC, and angle C is opposite AB
110^2=820^2+827^2-2*820*827*cos(A)
12,100=672,400+683,929-2*820*827*cos(A)
12,100=1,356,329-1,356,280cos(A)
1,356,280cos(A)=1,356,329-12,100
1,356,280cos(A)=1,344,229
cos(A)=1,344,229/1,356,280
cos(A)=0.9911147
angle A= between 7 degrees 39 minutes and 7 degrees 38 minutes
(0.991099)+(0.991138)/2=0.9911185 (approx. answer)
sine of 7 degrees 39 minutes=0.13312
sine of 7 degrees 38 minutes=0.13283
Theorem: The area of a triangle equals 1/2 the product of the lengths of two sides and the sine of their included angle.
A=(1/2)(820)(827(0.13312)
A=(1/2)(678,140)(0.13312)
A=(339,070)(0.13312)
A=45,136.998 sq ft
A=(339,070)(0.13283)
A=45,038.668 sq ft
45,137/43,560=1.0362 acres
45,038.67/43,560=1.0339 acres
1.0362*$2300=$2383.26 is the value of the land
1.0339*$2300=$2377.97 is the value of the land
if you take the average of the two values you get
$2383.26+$2377.97=$4761.23/2=$2380.62 for the value