Chapter 8.6, Problem 50PPS

To determine

To calculate:

The perimeter of given diagram.

Answer to Problem 50PPS

The perimeter of given diagram is $100.3$ .

Explanation of Solution

Given information:

  

Concept used:

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $a,b=$ sides

  $\cos C=$ angle

Calculation:

  

Let $x$ be the length of the third side of the triangle. Use the law of cosines to get the value of $x$ , since having the two sides and a nonincluded angle.

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $\begin{array}{l}a=152\\ b=88\\ c=x\\ \cos C={39}^{\circ }\end{array}$

First substitute,

  $x^2={\left(152\right)}^2+{\left(88\right)}^2-2\left(152\right)\left(88\right)\cos \left({39}^{\circ }\right)$

Now simplify,

  $x^2=23104+7744-20790.2$

Now take the square root of each side

  $x^2=\sqrt{10057.79}$

Now, simplify the root to get the value of $x$ ,

  $x\approx 100.3$

Hence, the perimeter of the diagram is $100.3$ .