# Chapter 3 - Problems - Page 111: 11

The distance from the starting point is 4.4 miles. The direction from the starting point is an angle of $58.1^{\circ}$ north of east.

#### Work Step by Step

We can find the total east component of the sum of the three parts of the hike: $0+(2.2~mi)~sin~35^{\circ} +(1.1~mi)~cos~15^{\circ} = 2.3~mi$ We can find the total north component of the sum of the three parts of the hike: $1.6~mi+(2.2~mi)~cos~35^{\circ} +(1.1~mi)~sin~15^{\circ} = 3.7~mi$ We can find the distance $d$ from the starting point: $d = \sqrt{(2.3~mi)^2+(3.7~mi)^2} = 4.4~mi$ We can find the direction north of east: $tan~\theta = \frac{3.7~mi}{2.3~mi}$ $\theta = tan^{-1}(\frac{3.7~mi}{2.3~mi})$ $\theta = 58.1^{\circ}$

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