# Chapter 2 - Acute Angles and Right Triangles - Section 2.5 Further Applications of Right Triangles - 2.5 Exercises - Page 87: 28

The distance from B to C is 352 miles

#### Work Step by Step

The points ABC form a triangle. We can find the angle at point A: $A = 180^{\circ}- 64^{\circ}-82^{\circ} = 34^{\circ}$ We can find the angle at point B: $B = 82^{\circ}- 26^{\circ} = 56^{\circ}$ We can find the angle at point C: $C = 180^{\circ}- 34^{\circ}-56^{\circ} = 90^{\circ}$ The triangle ABC is a right triangle. Let $c$ be the distance from A to B. We can find $c$: $c = (350~mph)(1.8~hr) = 630~mi$ Let $a$ be the distance from B to C. We can find $a$: $\frac{a}{c} = cos~56^{\circ}$ $a = (c)~(cos~56^{\circ})$ $a = (630~mi)~(cos~56^{\circ})$ $a = 352~mi$ The distance from B to C is 352 miles

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