Chapter 5.6, Problem 7CFU

To determine

To solve: If $B={17}^{\circ }55\text{'},C={98}^{\circ }15\text{'},a=17$ . Find c .

Answer to Problem 7CFU

  $c=18.7$

Explanation of Solution

Given information: $B={17}^{\circ }55\text{'},C={98}^{\circ }15\text{'},a=17$

Calculation:

We are given $\angle B={17}^{\circ }55\text{'},\angle C={98}^{\circ }15\text{'}$ and a = 17

Find c

First find $m\angle A$

The combine other two angles equals ${115}^{\circ }$ plus 70’ or ${116}^{\circ }10\text{'}$ since the sixty minutes turns into another degree.

So $\angle A={180}^{\circ }-{116}^{\circ }10\text{'}={63}^{\circ }50\text{'}$

Changing into this to decimal by dividing 50 by 60 gives us ${63.83}^{\circ }$ .

Use the law of sines, all we need is to compare a and c since that is all we are asked for, I’ve changed the 15 minutes to 0.25 degrees for angle C .

  $\begin{array}{l}\frac{17}{\sin {63.83}^{\circ }}=\frac{c}{\sin {98.25}^{\circ }}\\ c=\frac{17\times \sin {98.25}^{\circ }}{\sin {63.83}^{\circ }}\\ c=18.7\end{array}$