Chapter 6, Problem 7CT

To determine

The area of the parcel of landif a triangular parcel of land has borders of lengths 60 meters, 70 meters, and 82 meters.

Answer to Problem 7CT

Area of the parcel of land is $2052.526m^2$

Explanation of Solution

Given info:

  $a=60m,b=70m,c=82m$

Formula used:

  

Law of cosines

  $\begin{array}{l}\cos A=\frac{b^2+c^2-a^2}{2bc}\\ \cos B=\frac{a^2+c^2-b^2}{2ac}\\ \cos C=\frac{a^2+b^2-c^2}{2ab}\end{array}$

Area of triangle

  $A=\sqrt{s(s-a)(s-b)(s-c)},s=\frac{a+b+c}{2}$

Calculation:

Given that $a=60m,b=70m,c=82m$ , We have

  $\begin{array}{l}a=60m,b=70m,c=82m\\ A=\sqrt{s(s-a)(s-b)(s-c)}\\ s=\frac{a+b+c}{2}=\frac{60+70+82}{2}=106\\ A=\sqrt{106\times (106-60)\times (106-70)\times (106-82)}=2052.526m^2\end{array}$

Conclusion:

Thus,the area of the parcel of land is $2052.526m^2$