Chapter 12.6, Problem 4P

To determine

To determine the perimeter of the lot.

Answer to Problem 4P

The perimeter is 180m

Explanation of Solution

Given information :

Given angle is ${52}^{\circ }$

To find the perimeter we shall find the third side of the triangle.

  

Here we shall use the cosine rule.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

We will apply this three times for all three angles.

Hence we get,

  $\begin{array}{l}\cos {52}^{\circ }=\frac{{60}^2+{65}^2-B{C}^2}{2\left(60\right)\left(65\right)}\\ 4802.16=7825-B{C}^2\\ B{C}^2=3023\\ BC=55\end{array}$

Hence the perimeter is 55m+60m+65m =180m