{"id":1859,"date":"2019-08-16T13:41:15","date_gmt":"2019-08-16T17:41:15","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1859"},"modified":"2019-08-16T17:56:21","modified_gmt":"2019-08-16T21:56:21","slug":"answer-key-11-8","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-11-8\/","title":{"raw":"Answer Key 11.8","rendered":"Answer Key 11.8"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\nz^2&=&10^2+20^2-2(10)(20)\\text{ cos }40^{\\circ} \\\\\r\nz^2&=&100+400-306.4 \\\\\r\nz^2&=&193.6 \\\\ \\\\\r\nz&=&13.9\\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n20^2&=&28^2+28^2-2(28)(28)\\text{ cos }{\\O} \\\\ \\\\\r\n400&=&784+784-1568\\text{ cos }{\\O} \\\\ \\\\\r\n\\text{cos }{\\O}&=&\\dfrac{-1168}{-1568} \\\\ \\\\\r\n{\\O}&=&\\text{cos}^{-1}0.7449 \\\\ \\\\\r\n{\\O}&=&41.8^{\\circ}\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n140^2&=&200^2+130^2-2(200)(130)\\text{ cos }{\\O} \\\\ \\\\\r\n19600&=&400000+169000-52000\\text{ cos }{\\O} \\\\ \\\\\r\n\\text{cos }{\\O}&=&\\dfrac{-37300}{-52000} \\\\ \\\\\r\n{\\O}&=&\\text{cos}^{-1}0.71730 \\\\ \\\\\r\n{\\O}&=&44.2^{\\circ}\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\nx^2&=&125^2+120^2-2(125)(120)\\text{ cos }32^{\\circ} \\\\\r\nx^2&= &15625+14400-25441 \\\\\r\nx^2&=&4583.6 \\\\\r\nx&=&67.7\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n18^2&=&3^2+20^2-2(3)(20)\\text{ cos }{\\O} \\\\ \\\\\r\n324&=&9+400-120\\text{ cos }{\\O} \\\\ \\\\\r\n\\text{cos }{\\O}&=&\\dfrac{-85}{-120} \\\\ \\\\\r\n{\\O}&=&\\text{cos}^{-1}\\left(\\dfrac{-85}{-120}\\right) \\\\ \\\\\r\n{\\O}&=&44.9^{\\circ}\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{y}{\\text{sin }35^{\\circ}}&=&\\dfrac{40}{\\text{sin }65^{\\circ}} \\\\ \\\\\r\ny&=&\\dfrac{40\\text{ sin }35^{\\circ}}{\\text{sin }65^{\\circ}} \\\\ \\\\\r\ny&=&25.3\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{y}{\\text{sin }28^{\\circ}}&=&\\dfrac{12\\text{ m}}{\\text{sin }25^{\\circ}} \\\\ \\\\\r\ny&=&\\dfrac{12\\text{ sin }28^{\\circ}}{\\text{sin }25^{\\circ}} \\\\ \\\\\r\ny&=&13.3\\text{ m}\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\dfrac{x}{\\text{sin }25^{\\circ}}&=&\\dfrac{10\\text{ m}}{\\text{sin }15^{\\circ}} \\\\ \\\\\r\nx&=&\\dfrac{10\\text{ m sin }25^{\\circ}}{\\text{sin }15^{\\circ}} \\\\ \\\\\r\nx&=&16.3\\text{ m}\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{z}{\\text{sin }10^{\\circ}}&=&\\dfrac{8\\text{ cm}}{\\text{sin }70^{\\circ}} \\\\ \\\\\r\nz&=&\\dfrac{8\\text{ cm sin }10^{\\circ}}{\\text{sin }70^{\\circ}} \\\\ \\\\\r\nz&=&1.48\\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\ny^2&=&20^2+28^2-2(20)(28)\\text{ cos }130^{\\circ} \\\\\r\ny^2&=&400+784+720 \\\\\r\ny^2&=&1904 \\\\ \\\\\r\ny&=&43.6\\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n20^2&=&15^2+30^2-2(15)(30)\\text{ cos }{\\O} \\\\ \\\\\r\n400&=&225+900-900\\text{ cos }{\\O} \\\\ \\\\\r\n\\text{ cos }{\\O}&=&\\dfrac{-725}{-900} \\\\ \\\\\r\n{\\O}&=&\\text{cos}^{-1}\\left(\\dfrac{-725}{-900}\\right) \\\\ \\\\\r\n{\\O}&=&36.3^{\\circ}\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{x}{\\text{sin }95^{\\circ}}&=&\\dfrac{8\\text{ m}}{\\text{sin }20^{\\circ}} \\\\ \\\\\r\nx&=&\\dfrac{8\\text{ m sin }95^{\\circ}}{\\text{sin }20^{\\circ}} \\\\ \\\\\r\nx&=&23.3\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n16^2&=&10^2+8^2-2(8)(10)\\text{ cos}{\\O} \\\\ \\\\\r\n256&=&100+64-160\\text{ cos }{\\O} \\\\ \\\\\r\n\\text{ cos }{\\O}&=&\\dfrac{92}{-160} \\\\ \\\\\r\n{\\O}&=&\\text{ cos }^{-1}-0.575 \\\\ \\\\\r\n{\\O}&=&125^{\\circ}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\ny^2&=&20^2+24^2-2(20)(24)\\text{ cos }15^{\\circ} \\\\\r\ny^2&=&400+576-960\\text{ cos }15^{\\circ} \\\\\r\ny^2&=&976-927.3 \\\\\r\ny&=&\\sqrt{48.7} \\\\ \\\\\r\ny&=&6.98\\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n20^2&=&10^2+22^2-2(10)(22)\\text{ cos }{\\O} \\\\ \\\\\r\n400&=&100+484-440\\text{ cos }{\\O} \\\\ \\\\\r\n\\text{ cos }{\\O}&=&\\dfrac{-184}{-440} \\\\ \\\\\r\n{\\O}&=&\\text{cos}^{-1}\\left(\\dfrac{-184}{-440}\\right) \\\\ \\\\\r\n{\\O}&=&65.3^{\\circ}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{y}{\\text{sin }25^{\\circ}}&=&\\dfrac{20\\text{ m}}{\\text{sin }28^{\\circ}} \\\\ \\\\\r\ny&=&\\dfrac{20\\text{ m sin }25^{\\circ}}{\\text{sin }28^{\\circ}} \\\\ \\\\\r\ny&=&18\\text{ m}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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