Chapter 8.6, Problem 30PPS

To determine

To calculate:

The distance from Memphis to Huntsville.

Answer to Problem 30PPS

Memphis is about $207$ miles away from Huntsville.

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:

  

With the help of the above diagram it is easy to get the two sides and an included angle. So, with the help of the Law of cosines solve the issue.

First consider $x$ be the distance between Memphis and Huntsville.

Law of cosines:

  $c^2=a^2+b^2-2ab\cos C$

Where,

  $\begin{array}{l}a=90\\ b=122\\ \cos C=153.9\end{array}$

First substitute,

  $x^2={\left(90\right)}^2+{\left(122\right)}^2-2\left(90\right)\left(122\right)\cos \left(153.9\right)$

Now simplify,

  $x^2=42704.69$

Now take the square root of each side

  $x=\sqrt{42704.69}$

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

  $x\approx 207$

Hence, Memphis is about $207$ miles away from Huntsville.