{"id":2030,"date":"2021-12-02T19:40:33","date_gmt":"2021-12-03T00:40:33","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-8\/"},"modified":"2022-11-02T10:39:16","modified_gmt":"2022-11-02T14:39:16","slug":"answer-key-11-8","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-11-8\/","title":{"raw":"Answer Key 11.8","rendered":"Answer Key 11.8"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\nz^2&=&10^2+20^2-2(10)(20)\\text{ cos }40^{\\circ} \\\\\nz^2&=&100+400-306.4 \\\\\nz^2&=&193.6 \\\\ \\\\\nz&=&13.9\\text{ cm}\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n20^2&=&28^2+28^2-2(28)(28)\\text{ cos }{\\theta} \\\\ \\\\\n400&=&784+784-1568\\text{ cos }{\\theta} \\\\ \\\\\n\\text{cos }{\\theta}&=&\\dfrac{-1168}{-1568} \\\\ \\\\\n{\\theta}&=&\\text{cos}^{-1}0.7449 \\\\ \\\\\n{\\theta}&=&41.8^{\\circ}\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n140^2&=&200^2+130^2-2(200)(130)\\text{ cos }{\\theta} \\\\ \\\\\n19600&=&400000+169000-52000\\text{ cos }{\\theta} \\\\ \\\\\n\\text{cos }{\\theta}&=&\\dfrac{-37300}{-52000} \\\\ \\\\\n{\\theta}&=&\\text{cos}^{-1}0.71730 \\\\ \\\\\n{\\theta}&=&44.2^{\\circ}\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\nx^2&=&125^2+120^2-2(125)(120)\\text{ cos }32^{\\circ} \\\\\nx^2&= &15625+14400-25441 \\\\\nx^2&=&4583.6 \\\\\nx&=&67.7\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n18^2&=&3^2+20^2-2(3)(20)\\text{ cos }{\\theta} \\\\ \\\\\n324&=&9+400-120\\text{ cos }{\\theta} \\\\ \\\\\n\\text{cos }{\\theta}&=&\\dfrac{-85}{-120} \\\\ \\\\\n{\\theta}&=&\\text{cos}^{-1}\\left(\\dfrac{-85}{-120}\\right) \\\\ \\\\\n{\\theta}&=&44.9^{\\circ}\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{y}{\\text{sin }35^{\\circ}}&=&\\dfrac{40}{\\text{sin }65^{\\circ}} \\\\ \\\\\ny&=&\\dfrac{40\\text{ sin }35^{\\circ}}{\\text{sin }65^{\\circ}} \\\\ \\\\\ny&=&25.3\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{y}{\\text{sin }28^{\\circ}}&=&\\dfrac{12\\text{ m}}{\\text{sin }25^{\\circ}} \\\\ \\\\\ny&=&\\dfrac{12\\text{ sin }28^{\\circ}}{\\text{sin }25^{\\circ}} \\\\ \\\\\ny&=&13.3\\text{ m}\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{x}{\\text{sin }25^{\\circ}}&=&\\dfrac{10\\text{ m}}{\\text{sin }15^{\\circ}} \\\\ \\\\\nx&=&\\dfrac{10\\text{ m sin }25^{\\circ}}{\\text{sin }15^{\\circ}} \\\\ \\\\\nx&=&16.3\\text{ m}\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{z}{\\text{sin }10^{\\circ}}&=&\\dfrac{8\\text{ cm}}{\\text{sin }70^{\\circ}} \\\\ \\\\\nz&=&\\dfrac{8\\text{ cm sin }10^{\\circ}}{\\text{sin }70^{\\circ}} \\\\ \\\\\nz&=&1.48\\text{ cm}\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\ny^2&=&20^2+28^2-2(20)(28)\\text{ cos }130^{\\circ} \\\\\ny^2&=&400+784+720 \\\\\ny^2&=&1904 \\\\ \\\\\ny&=&43.6\\text{ cm}\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n20^2&=&15^2+30^2-2(15)(30)\\text{ cos }{\\theta} \\\\ \\\\\n400&=&225+900-900\\text{ cos }{\\theta} \\\\ \\\\\n\\text{ cos }{\\theta}&=&\\dfrac{-725}{-900} \\\\ \\\\\n{\\theta}&=&\\text{cos}^{-1}\\left(\\dfrac{-725}{-900}\\right) \\\\ \\\\\n{\\theta}&=&36.3^{\\circ}\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{x}{\\text{sin }95^{\\circ}}&=&\\dfrac{8\\text{ m}}{\\text{sin }20^{\\circ}} \\\\ \\\\\nx&=&\\dfrac{8\\text{ m sin }95^{\\circ}}{\\text{sin }20^{\\circ}} \\\\ \\\\\nx&=&23.3\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n16^2&=&10^2+8^2-2(8)(10)\\text{ cos}{\\theta} \\\\ \\\\\n256&=&100+64-160\\text{ cos }{\\theta} \\\\ \\\\\n\\text{ cos }{\\theta}&=&\\dfrac{92}{-160} \\\\ \\\\\n{\\theta}&=&\\text{ cos }^{-1}-0.575 \\\\ \\\\\n{\\theta}&=&125^{\\circ}\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\ny^2&=&20^2+24^2-2(20)(24)\\text{ cos }15^{\\circ} \\\\\ny^2&=&400+576-960\\text{ cos }15^{\\circ} \\\\\ny^2&=&976-927.3 \\\\\ny&=&\\sqrt{48.7} \\\\ \\\\\ny&=&6.98\\text{ cm}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n20^2&=&10^2+22^2-2(10)(22)\\text{ cos }{\\theta} \\\\ \\\\\n400&=&100+484-440\\text{ cos }{\\theta} \\\\ \\\\\n\\text{ cos }{\\theta}&=&\\dfrac{-184}{-440} \\\\ \\\\\n{\\theta}&=&\\text{cos}^{-1}\\left(\\dfrac{-184}{-440}\\right) \\\\ \\\\\n{\\theta}&=&65.3^{\\circ}\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n\\dfrac{y}{\\text{sin }25^{\\circ}}&=&\\dfrac{20\\text{ m}}{\\text{sin }28^{\\circ}} \\\\ \\\\\ny&=&\\dfrac{20\\text{ m sin }25^{\\circ}}{\\text{sin }28^{\\circ}} \\\\ \\\\\ny&=&18\\text{ m}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} z^2&=&10^2+20^2-2(10)(20)\\text{ cos }40^{\\circ} \\\\ z^2&=&100+400-306.4 \\\\ z^2&=&193.6 \\\\ \\\\ z&=&13.9\\text{ cm} \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 20^2&=&28^2+28^2-2(28)(28)\\text{ cos }{\\theta} \\\\ \\\\ 400&=&784+784-1568\\text{ cos }{\\theta} \\\\ \\\\ \\text{cos }{\\theta}&=&\\dfrac{-1168}{-1568} \\\\ \\\\ {\\theta}&=&\\text{cos}^{-1}0.7449 \\\\ \\\\ {\\theta}&=&41.8^{\\circ} \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 140^2&=&200^2+130^2-2(200)(130)\\text{ cos }{\\theta} \\\\ \\\\ 19600&=&400000+169000-52000\\text{ cos }{\\theta} \\\\ \\\\ \\text{cos }{\\theta}&=&\\dfrac{-37300}{-52000} \\\\ \\\\ {\\theta}&=&\\text{cos}^{-1}0.71730 \\\\ \\\\ {\\theta}&=&44.2^{\\circ} \\end{array}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} x^2&=&125^2+120^2-2(125)(120)\\text{ cos }32^{\\circ} \\\\ x^2&= &15625+14400-25441 \\\\ x^2&=&4583.6 \\\\ x&=&67.7 \\end{array}[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 18^2&=&3^2+20^2-2(3)(20)\\text{ cos }{\\theta} \\\\ \\\\ 324&=&9+400-120\\text{ cos }{\\theta} \\\\ \\\\ \\text{cos }{\\theta}&=&\\dfrac{-85}{-120} \\\\ \\\\ {\\theta}&=&\\text{cos}^{-1}\\left(\\dfrac{-85}{-120}\\right) \\\\ \\\\ {\\theta}&=&44.9^{\\circ} \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{y}{\\text{sin }35^{\\circ}}&=&\\dfrac{40}{\\text{sin }65^{\\circ}} \\\\ \\\\ y&=&\\dfrac{40\\text{ sin }35^{\\circ}}{\\text{sin }65^{\\circ}} \\\\ \\\\ y&=&25.3 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{y}{\\text{sin }28^{\\circ}}&=&\\dfrac{12\\text{ m}}{\\text{sin }25^{\\circ}} \\\\ \\\\ y&=&\\dfrac{12\\text{ sin }28^{\\circ}}{\\text{sin }25^{\\circ}} \\\\ \\\\ y&=&13.3\\text{ m} \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{x}{\\text{sin }25^{\\circ}}&=&\\dfrac{10\\text{ m}}{\\text{sin }15^{\\circ}} \\\\ \\\\ x&=&\\dfrac{10\\text{ m sin }25^{\\circ}}{\\text{sin }15^{\\circ}} \\\\ \\\\ x&=&16.3\\text{ m} \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{z}{\\text{sin }10^{\\circ}}&=&\\dfrac{8\\text{ cm}}{\\text{sin }70^{\\circ}} \\\\ \\\\ z&=&\\dfrac{8\\text{ cm sin }10^{\\circ}}{\\text{sin }70^{\\circ}} \\\\ \\\\ z&=&1.48\\text{ cm} \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} y^2&=&20^2+28^2-2(20)(28)\\text{ cos }130^{\\circ} \\\\ y^2&=&400+784+720 \\\\ y^2&=&1904 \\\\ \\\\ y&=&43.6\\text{ cm} \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 20^2&=&15^2+30^2-2(15)(30)\\text{ cos }{\\theta} \\\\ \\\\ 400&=&225+900-900\\text{ cos }{\\theta} \\\\ \\\\ \\text{ cos }{\\theta}&=&\\dfrac{-725}{-900} \\\\ \\\\ {\\theta}&=&\\text{cos}^{-1}\\left(\\dfrac{-725}{-900}\\right) \\\\ \\\\ {\\theta}&=&36.3^{\\circ} \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{x}{\\text{sin }95^{\\circ}}&=&\\dfrac{8\\text{ m}}{\\text{sin }20^{\\circ}} \\\\ \\\\ x&=&\\dfrac{8\\text{ m sin }95^{\\circ}}{\\text{sin }20^{\\circ}} \\\\ \\\\ x&=&23.3 \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 16^2&=&10^2+8^2-2(8)(10)\\text{ cos}{\\theta} \\\\ \\\\ 256&=&100+64-160\\text{ cos }{\\theta} \\\\ \\\\ \\text{ cos }{\\theta}&=&\\dfrac{92}{-160} \\\\ \\\\ {\\theta}&=&\\text{ cos }^{-1}-0.575 \\\\ \\\\ {\\theta}&=&125^{\\circ} \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} y^2&=&20^2+24^2-2(20)(24)\\text{ cos }15^{\\circ} \\\\ y^2&=&400+576-960\\text{ cos }15^{\\circ} \\\\ y^2&=&976-927.3 \\\\ y&=&\\sqrt{48.7} \\\\ \\\\ y&=&6.98\\text{ cm} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 20^2&=&10^2+22^2-2(10)(22)\\text{ cos }{\\theta} \\\\ \\\\ 400&=&100+484-440\\text{ cos }{\\theta} \\\\ \\\\ \\text{ cos }{\\theta}&=&\\dfrac{-184}{-440} \\\\ \\\\ {\\theta}&=&\\text{cos}^{-1}\\left(\\dfrac{-184}{-440}\\right) \\\\ \\\\ {\\theta}&=&65.3^{\\circ} \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} \\dfrac{y}{\\text{sin }25^{\\circ}}&=&\\dfrac{20\\text{ m}}{\\text{sin }28^{\\circ}} \\\\ \\\\ y&=&\\dfrac{20\\text{ m sin }25^{\\circ}}{\\text{sin }28^{\\circ}} \\\\ \\\\ y&=&18\\text{ m} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":114,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-2030","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2030","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2030\/revisions"}],"predecessor-version":[{"id":2031,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2030\/revisions\/2031"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2030\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2030"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2030"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2030"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}