Answer Key 11.7

[latexpage]

1. 0.743145
2. 0.484810
3. 0.906308
4. 0.484810
5. 0.194380
6. 1.53986
7. 0.190810
8. 0.544639
9. 29°
10. 39°
11. 50°
12. 52°
13. 33.3°
14. 8.9°
15. 41°
16. 81°

1. \(\begin{array}{ll}
   \\ \\
   \begin{array}{rrl}
   \\ \\
   20^2+10^2&=&z^2 \\ \\
   z&=&\sqrt{500} \\ \\
   z&=&22.36\dots
   \end{array}
   &\hspace{0.5in}
   \begin{array}{rrl}
   \\ \\ \\ \\
   \text{tan }{\O}&=&\dfrac{\text{opp}}{\text{adj}} \\ \\
   \text{tan }{\O}&=&\dfrac{10}{20} \\ \\
   {\O}&=&\text{tan }^{-1} 0.5 \\ \\
   {\O}&=&26.6^{\circ}
   \end{array}
   \end{array}\)
2. \(\begin{array}{ll}
   \\ \\ \\
   \begin{array}{rrl}
   \\ \\ \\
   20^2+y^2&=&28^2 \\ \\
   y&=&\sqrt{28^2-20^2} \\ \\
   y&=&\sqrt{384} \\ \\
   y&=&19.6
   \end{array}
   &\hspace{0.5in}
   \begin{array}{rrl}
   \\ \\ \\ \\
   \text{cos }{\O}&=&\dfrac{A}{H} \\ \\
   \text{cos }{\O}&=&\dfrac{20}{28} \\ \\
   {\O}&=&\text{cos }^{-1} \left(\dfrac{20}{28}\right) \\ \\
   {\O}&=&44.4^{\circ}
   \end{array}
   \end{array}\)
3. \(\begin{array}{ll}
   \\ \\ \\
   \begin{array}{rrl}
   \\ \\ \\ \\
   \text{cos }{\O}&=&\dfrac{A}{H} \\ \\
   \text{cos }{\O}&=&\dfrac{12}{20} \\ \\
   {\O}&=&\text{cos }^{-1} \left(\dfrac{12}{20}\right) \\ \\
   {\O}&=&53.1^{\circ}
   \end{array}
   &\hspace{0.5in}
   \begin{array}{rrl}
   12^2+x^2&=&20^2 \\ \\
   x&=&\sqrt{20^2-12^2} \\ \\
   x&=&16
   \end{array}
   \end{array}\)
4. \(\begin{array}{ll}
   \\ \\ \\ \\
   \begin{array}{rrl}
   \text{cos }32&=&\dfrac{x}{25} \\ \\
   x&=&25\text{ cos }32 \\ \\
   x&=&21.2
   \end{array}
   &\hspace{0.5in}
   \begin{array}{rrl}
   \text{sin }32^{\circ}&=&\dfrac{y}{25} \\ \\
   y&=&25\text{ sin }32 \\ \\
   y&=&13.2
   \end{array}
   \end{array}\)
5. \(\begin{array}{ll}
   \\ \\ \\ \\
   \begin{array}{rrl}
   \text{cos }42^{\circ}&=&\dfrac{x}{1200N} \\ \\
   x&=&1200N\text{ cos }42^{\circ} \\ \\
   x&=&891.8 N
   \end{array}
   & \hspace{0.5in}
   \begin{array}{rrl}
   \text{sin }42^{\circ}&=&\dfrac{y}{1200N} \\ \\
   y&=&1200N\text{ sin }42^{\circ} \\ \\
   y&=&803N
   \end{array}
   \end{array}\)
6. \(\begin{array}{ll}
   \\ \\ \\ \\ \\
   \begin{array}{rrl}
   \text{tan }{\O}&=&\dfrac{100N}{220N} \\ \\
   {\O}&=&\text{tan}^{-1}\left(\dfrac{100}{220}\right) \\ \\
   {\O}&=&24.4^{\circ}
   \end{array}
   &\hspace{0.5in}
   \begin{array}{rrl}
   z^2&=&100^2+220^2 \\ \\
   z&=&\sqrt{58400} \\ \\
   z&=&241.7
   \end{array}
   \end{array}\)
7. \(\begin{array}{ll}
   \\ \\ \\ \\
   \begin{array}{rrl}
   \text{cos }55^{\circ}&=&\dfrac{y}{12} \\ \\
   y&=&12\text{ cos }55^{\circ} \\ \\
   y&=&6.9
   \end{array}
   &\hspace{0.5in}
   \begin{array}{rrl}
   \text{sin }55^{\circ}&=&\dfrac{x}{12} \\ \\
   x&=&12\text{ sin }55^{\circ} \\ \\
   x&=&9.8
   \end{array}
   \end{array}\)
8. \(\begin{array}{ll}
   \\ \\ \\ \\
   \begin{array}{rrl}
   \text{tan }28&=&\dfrac{20}{x} \\ \\
   x&=&\dfrac{20}{\text{tan }28} \\ \\
   x&=&37.6
   \end{array}
   &\hspace{0.5in}
   \begin{array}{rrl}
   \text{sin }28^{\circ}&=&\dfrac{20}{z} \\ \\
   z&=&\dfrac{20}{\text{sin }28} \\ \\
   z&=&42.6
   \end{array}
   \end{array}\)
9. \(\begin{array}{ll}
   \\ \\ \\ \\ \\
   \begin{array}{rrl}
   \text{tan }{\O}&=&\dfrac{20}{15} \\ \\
   {\O}&=&\text{tan}^{-1}\left(\dfrac{20}{15}\right) \\ \\
   {\O}&=&53.1^{\circ}
   \end{array}
   & \hspace{0.5in}
   \begin{array}{rrl}
   15^2+20^2&=&z^2 \\ \\
   z&=&\sqrt{625} \\ \\
   z&=&25
   \end{array}
   \end{array}\)
10. \(\begin{array}{ll}
    \\ \\ \\ \\
    \begin{array}{rrl}
    y^2+100^2&=&125^2 \\ \\
    y&=&\sqrt{125^2-100^2} \\ \\
    y&=&75
    \end{array}
    &\hspace{0.5in}
    \begin{array}{rrl}
    \text{cos }{\O}&=&\dfrac{100}{125} \\ \\
    {\O}&=&\text{cos}^{-1}\left(\dfrac{100}{125}\right) \\ \\
    {\O}&=&36.9^{\circ}
    \end{array}
    \end{array}\)
11. \(\begin{array}{ll}
    \\ \\ \\ \\ \\
    \begin{array}{rrl}
    \text{cos }{\O}&=&\dfrac{3}{5} \\ \\
    {\O}&=&\text{cos }^{-1}\left(\dfrac{3}{5}\right) \\ \\
    {\O}&=&53.1
    \end{array}
    & \hspace{0.5in}
    \begin{array}{rrl}
    3^2+y^2&=&5^2 \\ \\
    y&=&\sqrt{5^2-3^2} \\ \\
    y&=&4
    \end{array}
    \end{array}\)
12. \(\begin{array}{ll}
    \\ \\ \\ \\
    \begin{array}{rrl}
    \text{cos }24^{\circ}&=&\dfrac{25}{z} \\ \\
    z&=&\dfrac{25}{\text{cos }24^{\circ}} \\ \\
    z&=&27.4
    \end{array}
    & \hspace{0.5in}
    \begin{array}{rrl}
    \text{tan }24^{\circ}&=&\dfrac{y}{25} \\ \\
    y&=&25\text{ tan }24^{\circ} \\ \\
    y&=&11.1
    \end{array}
    \end{array}\)
13. \(\begin{array}{ll}
    \\ \\ \\ \\ \\
    \begin{array}{rrl}
    \text{sin }{\O}&=&\dfrac{28}{40} \\ \\
    {\O}&=&\text{sin }^{-1}\left(\dfrac{28}{40}\right) \\ \\
    {\O}&=&44.4^{\circ}
    \end{array}
    &\hspace{0.25in}
    \begin{array}{rrl}
    z^2+28^2&=&40^2 \\ \\
    z&=&\sqrt{40^2-28^2} \\ \\
    z&=&28.6
    \end{array}
    \end{array}\)
14. \(\begin{array}{ll}
    \\ \\ \\ \\ \\
    \begin{array}{rrl}
    \text{cos }{\O}&=&\dfrac{20}{28} \\ \\
    {\O}&=&\text{cos }^{-1}\left(\dfrac{20}{28}\right) \\ \\
    {\O}&=&44.4^{\circ}
    \end{array}
    & \hspace{0.5in}
    \begin{array}{rrl}
    20^2+y^2&=&28^2 \\ \\
    y&=&\sqrt{28^2-20^2} \\ \\
    y&=&19.6
    \end{array}
    \end{array}\)
15. \(\begin{array}{ll}
    \\ \\ \\ \\ \\
    \begin{array}{rrl}
    \text{sin }{\O}&=&\dfrac{8}{12} \\ \\
    {\O}&=&\text{sin}^{-1}\left(\dfrac{8}{12}\right) \\ \\
    {\O}&=&41.8^{\circ}
    \end{array}
    & \hspace{0.5in}
    \begin{array}{rrl}
    y^2+8^2&=&12^2 \\ \\
    y&=&\sqrt{12^2-8^2} \\ \\
    y&=&8.9
    \end{array}
    \end{array}\)
16. \(\begin{array}{ll}
    \\ \\ \\ \\
    \begin{array}{rrl}
    \text{tan }35^{\circ}&=&\dfrac{x}{50} \\ \\
    x&=&50\text{ tan }35^{\circ} \\ \\
    x&=&35
    \end{array}
    &\hspace{0.5in}
    \begin{array}{rrl}
    \text{cos }35^{\circ}&=&\dfrac{50}{y} \\ \\
    y&=&\dfrac{50}{\text{cos }35^{\circ}} \\ \\
    y&=&61
    \end{array}
    \end{array}\)