Chapter 12.5, Problem 3GP

To determine

To find: To find the length from the starting point to the last point for Amelia as she ran 6 miles in one direction then turned 79 degree and ran 7 miles.

Answer to Problem 3GP

The length between the first and last point of Amelia is 8.3 miles.

Explanation of Solution

Given information:

As per the question if we draw triangle for first, second and last point of the Amelia-

Given in triangle ABC

  AB= c= 6 miles

  BC= a= 7 miles

  $\angle ABC={79}^{\circ }$

Calculation:

To find the length of side AC, we use the cosine formula for any triangle:

  $b^2=a^2+c^2-2ac\cos B$

Let AC=b

  AB = c = 6

  BC = a = 7

  $\begin{array}{l}\angle ABC={79}^{\circ }\\ \\ b^2=6^2+7^2-2\times 6\times 7\cos {79}^{\circ }\\ \Rightarrow b^2=36+49-84\times (\text{0}\text{.190809})\\ \Rightarrow b^2=85-16.03\\ \Rightarrow b^2=68.97\\ \Rightarrow b=\sqrt{68.97}\\ \Rightarrow b=8.3\end{array}$

So the length between the first and last point of Amelia is 8.3 miles.