Answer Key 11.7

  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}

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