Chapter 4

1. $\begin{array}{rcl} - 165 ° + 360 ° & = & 195 ° \\ - 165 ° - 360 ° & = & - 525 ° \end{array}$ $\begin{array}{rcl} - 165 ° + 360 ° & = & 195 ° \\ - 165 ° - 360 ° & = & - 525 ° \end{array}$
2. $\begin{array}{l} 3 9^{'} = (\frac{39}{60}) ° = 0.65 ° \\ 37 ° 3 9^{'} = 37.65 ° \end{array}$ $\begin{array}{l} 3 9^{'} = (\frac{39}{60}) ° = 0.65 ° \\ 37 ° 3 9^{'} = 37.65 ° \end{array}$
3. $\tan 73.8 ° = 3.44$ $\tan 73.8 ° = 3.44$
4. $\cos θ = 0.3726; θ = 68.12 °$ $\cos θ = 0.3726; θ = 68.12 °$
5. $\begin{array}{rcl} Let x & = & distance from course to east \\ \frac{x}{22.62} & = & \sin 4.05 ° \\ x & = & 22.62 \sin 4.05 ° \\ = & 1.598 km \end{array}$ $\begin{array}{rcl} Let x & = & distance from course to east \\ \frac{x}{22.62} & = & \sin 4.05 ° \\ x & = & 22.62 \sin 4.05 ° \\ = & 1.598 km \end{array}$
6. $\begin{array}{l} \sin θ = \frac{2}{3} \\ x = \sqrt{3^{2} - 2^{2}} = \sqrt{5} \\ \tan θ = \frac{2}{\sqrt{5}} \end{array}$ $\begin{array}{l} \sin θ = \frac{2}{3} \\ x = \sqrt{3^{2} - 2^{2}} = \sqrt{5} \\ \tan θ = \frac{2}{\sqrt{5}} \end{array}$
7. $\tan θ = 1.294; \csc θ = 1.264$ $\tan θ = 1.294; \csc θ = 1.264$
8. $\begin{array}{rclrcl} B & = & 90 ° - 37.4 ° = 52.6 ° & \frac{52.8}{c} & = & \cos 37.4 ° \\ \frac{a}{52.8} & = & \tan 37.4 ° & c & = & \frac{52.8}{\cos 37.4 °} \\ a & = & 52.8 \tan 37.4 ° & = & 66.5 \\ = & 40.4 \end{array}$ $\begin{array}{rclrcl} B & = & 90 ° - 37.4 ° = 52.6 ° & \frac{52.8}{c} & = & \cos 37.4 ° \\ \frac{a}{52.8} & = & \tan 37.4 ° & c & = & \frac{52.8}{\cos 37.4 °} \\ a & = & 52.8 \tan 37.4 ° & = & 66.5 \\ = & 40.4 \end{array}$
9. $\begin{array}{l} {2.49}^{2} + b^{2} = {3.88}^{2} \\ b = \sqrt{{3.88}^{2} - {2.49}^{2}} = 2.98 \\ \sin A = \frac{2.49}{3.88} \\ A = \sin^{- 1} (\frac{2.49}{3.88}) \\ A = 39.9 ° B = 50.1 ° \end{array}$ $\begin{array}{l} {2.49}^{2} + b^{2} = {3.88}^{2} \\ b = \sqrt{{3.88}^{2} - {2.49}^{2}} = 2.98 \\ \sin A = \frac{2.49}{3.88} \\ A = \sin^{- 1} (\frac{2.49}{3.88}) \\ A = 39.9 ° B = 50.1 ° \end{array}$
10. $\begin{array}{l} \frac{s / 2}{12.0} = \cos 42.0 ° \\ s = 24.0 \cos 42.0 ° = 17.8 \end{array}$ $\begin{array}{l} \frac{s / 2}{12.0} = \cos 42.0 ° \\ s = 24.0 \cos 42.0 ° = 17.8 \end{array}$
11.

$\begin{array}{l} h = \sqrt{9^{2} + 40^{2}} = 41 \\ \sin θ = \frac{9}{41}, \cos θ = \frac{40}{41} \\ \frac{\sin θ}{\cos θ} = \frac{9/41}{40/41} = \frac{9}{40} \end{array}$ $\begin{array}{l} h = \sqrt{9^{2} + 40^{2}} = 41 \\ \sin θ = \frac{9}{41}, \cos θ = \frac{40}{41} \\ \frac{\sin θ}{\cos θ} = \frac{9/41}{40/41} = \frac{9}{40} \end{array}$
12. $\begin{array}{rcl} λ & = & d \sin θ \\ = & 30.05 \sin 1.167 ° \\ = & 0.6120 μ m \end{array}$ $\begin{array}{rcl} λ & = & d \sin θ \\ = & 30.05 \sin 1.167 ° \\ = & 0.6120 μ m \end{array}$
13. $\begin{array}{l} r = \sqrt{5^{2} + 2^{2}} = \sqrt{29} \\ \begin{array}{l} \sin θ = \frac{2}{\sqrt{29}} = 0.3714 & \csc θ = \frac{\sqrt{29}}{2} = 2.693 \\ \cos θ = \frac{5}{\sqrt{29}} = 0.9285 & sec θ = \frac{\sqrt{29}}{5} = 1.077 \\ \tan θ = \frac{2}{5} = 0.4000 & cot θ = \frac{5}{2} = 2.500 \end{array} \end{array}$ $\begin{array}{l} r = \sqrt{5^{2} + 2^{2}} = \sqrt{29} \\ \begin{array}{l} \sin θ = \frac{2}{\sqrt{29}} = 0.3714 & \csc θ = \frac{\sqrt{29}}{2} = 2.693 \\ \cos θ = \frac{5}{\sqrt{29}} = 0.9285 & sec θ = \frac{\sqrt{29}}{5} = 1.077 \\ \tan θ = \frac{2}{5} = 0.4000 & cot θ = \frac{5}{2} = 2.500 \end{array} \end{array}$
14. Let $x = new$ $x = new$ length of ramp

$\begin{array}{l} \sin 4.50 ° = \frac{2.50}{x} \\ x = \frac{2.50}{\sin 4.50 °} = 31.9 ft \\ added length = 31.9 - 9.5 = 22.4 ft \end{array}$ $\begin{array}{l} \sin 4.50 ° = \frac{2.50}{x} \\ x = \frac{2.50}{\sin 4.50 °} = 31.9 ft \\ added length = 31.9 - 9.5 = 22.4 ft \end{array}$
15. Distance between points is $x - y .$ $x - y .$

$\begin{array}{l} \frac{18.525}{x} = \tan 13.500 ° \frac{18.525}{y} = \tan 21.375 ° \\ x - y = \frac{18.525}{\tan 13.500 °} - \frac{18.525}{\tan 21.375} ° = 29.831 m \end{array}$ $\begin{array}{l} \frac{18.525}{x} = \tan 13.500 ° \frac{18.525}{y} = \tan 21.375 ° \\ x - y = \frac{18.525}{\tan 13.500 °} - \frac{18.525}{\tan 21.375} ° = 29.831 m \end{array}$

1-1 Full Alternative Text