# Chapter 13 - Section 13.3 - Using Trigonometric Ratios to Find Sides - Exercise - Page 458: 8

$$b=38km$$ $$c=42.6km$$

#### Work Step by Step

To find side b, we can use the trigonometric ratio for tangent $tanB=\frac{b}{a}$ Where $B=63.2°$ $a=19.2km$ Solving for b we get: $b=a*tanB$ $b=19.2km*tan(63.2°)$ $b=19.2km*1.9797$ $b=38km$ To find side c (the hypotenuse), we can use the trigonometric ratio for cosine. $cosB=\frac{a}{c}$ Where $B=63.2°$ $a=19.2km$ Solving for c we get: $c=\frac{a}{cosB}$ $c=\frac{19.2km}{cos(63.2°)}$ $c=\frac{19.2km}{0.4509}$ $c=42.6km$

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