{"id":1852,"date":"2019-08-15T18:39:03","date_gmt":"2019-08-15T22:39:03","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1852"},"modified":"2019-08-16T11:43:44","modified_gmt":"2019-08-16T15:43:44","slug":"answer-key-11-7","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-11-7\/","title":{"raw":"Answer Key 11.7","rendered":"Answer Key 11.7"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. 0.743145<\/li>\r\n \t
  2. 0.484810<\/li>\r\n \t
  3. 0.906308<\/li>\r\n \t
  4. 0.484810<\/li>\r\n \t
  5. 0.194380<\/li>\r\n \t
  6. 1.53986<\/li>\r\n \t
  7. 0.190810<\/li>\r\n \t
  8. 0.544639<\/li>\r\n \t
  9. 29\u00b0<\/li>\r\n \t
  10. 39\u00b0<\/li>\r\n \t
  11. 50\u00b0<\/li>\r\n \t
  12. 52\u00b0<\/li>\r\n \t
  13. 33.3\u00b0<\/li>\r\n \t
  14. 8.9\u00b0<\/li>\r\n \t
  15. 41\u00b0<\/li>\r\n \t
  16. 81\u00b0<\/li>\r\n<\/ol>\r\n \r\n
      \r\n \t
    1. \\(\\begin{array}{ll}\r\n\\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\\r\n20^2+10^2&=&z^2 \\\\ \\\\\r\nz&=&\\sqrt{500} \\\\ \\\\\r\nz&=&22.36\\dots\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\text{tan }{\\O}&=&\\dfrac{\\text{opp}}{\\text{adj}} \\\\ \\\\\r\n\\text{tan }{\\O}&=&\\dfrac{10}{20} \\\\ \\\\\r\n{\\O}&=&\\text{tan }^{-1} 0.5 \\\\ \\\\\r\n{\\O}&=&26.6^{\\circ}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    2. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n20^2+y^2&=&28^2 \\\\ \\\\\r\ny&=&\\sqrt{28^2-20^2} \\\\ \\\\\r\ny&=&\\sqrt{384} \\\\ \\\\\r\ny&=&19.6\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\text{cos }{\\O}&=&\\dfrac{A}{H} \\\\ \\\\\r\n\\text{cos }{\\O}&=&\\dfrac{20}{28} \\\\ \\\\\r\n{\\O}&=&\\text{cos }^{-1} \\left(\\dfrac{20}{28}\\right) \\\\ \\\\\r\n{\\O}&=&44.4^{\\circ}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    3. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\text{cos }{\\O}&=&\\dfrac{A}{H} \\\\ \\\\\r\n\\text{cos }{\\O}&=&\\dfrac{12}{20} \\\\ \\\\\r\n{\\O}&=&\\text{cos }^{-1} \\left(\\dfrac{12}{20}\\right) \\\\ \\\\\r\n{\\O}&=&53.1^{\\circ}\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n12^2+x^2&=&20^2 \\\\ \\\\\r\nx&=&\\sqrt{20^2-12^2} \\\\ \\\\\r\nx&=&16\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    4. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{cos }32&=&\\dfrac{x}{25} \\\\ \\\\\r\nx&=&25\\text{ cos }32 \\\\ \\\\\r\nx&=&21.2\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\text{sin }32^{\\circ}&=&\\dfrac{y}{25} \\\\ \\\\\r\ny&=&25\\text{ sin }32 \\\\ \\\\\r\ny&=&13.2\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    5. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{cos }42^{\\circ}&=&\\dfrac{x}{1200N} \\\\ \\\\\r\nx&=&1200N\\text{ cos }42^{\\circ} \\\\ \\\\\r\nx&=&891.8 N\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\text{sin }42^{\\circ}&=&\\dfrac{y}{1200N} \\\\ \\\\\r\ny&=&1200N\\text{ sin }42^{\\circ} \\\\ \\\\\r\ny&=&803N\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    6. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{tan }{\\O}&=&\\dfrac{100N}{220N} \\\\ \\\\\r\n{\\O}&=&\\text{tan}^{-1}\\left(\\dfrac{100}{220}\\right) \\\\ \\\\\r\n{\\O}&=&24.4^{\\circ}\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\nz^2&=&100^2+220^2 \\\\ \\\\\r\nz&=&\\sqrt{58400} \\\\ \\\\\r\nz&=&241.7\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    7. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{cos }55^{\\circ}&=&\\dfrac{y}{12} \\\\ \\\\\r\ny&=&12\\text{ cos }55^{\\circ} \\\\ \\\\\r\ny&=&6.9\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\text{sin }55^{\\circ}&=&\\dfrac{x}{12} \\\\ \\\\\r\nx&=&12\\text{ sin }55^{\\circ} \\\\ \\\\\r\nx&=&9.8\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    8. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{tan }28&=&\\dfrac{20}{x} \\\\ \\\\\r\nx&=&\\dfrac{20}{\\text{tan }28} \\\\ \\\\\r\nx&=&37.6\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\text{sin }28^{\\circ}&=&\\dfrac{20}{z} \\\\ \\\\\r\nz&=&\\dfrac{20}{\\text{sin }28} \\\\ \\\\\r\nz&=&42.6\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    9. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{tan }{\\O}&=&\\dfrac{20}{15} \\\\ \\\\\r\n{\\O}&=&\\text{tan}^{-1}\\left(\\dfrac{20}{15}\\right) \\\\ \\\\\r\n{\\O}&=&53.1^{\\circ}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n15^2+20^2&=&z^2 \\\\ \\\\\r\nz&=&\\sqrt{625} \\\\ \\\\\r\nz&=&25\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    10. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\ny^2+100^2&=&125^2 \\\\ \\\\\r\ny&=&\\sqrt{125^2-100^2} \\\\ \\\\\r\ny&=&75\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\text{cos }{\\O}&=&\\dfrac{100}{125} \\\\ \\\\\r\n{\\O}&=&\\text{cos}^{-1}\\left(\\dfrac{100}{125}\\right) \\\\ \\\\\r\n{\\O}&=&36.9^{\\circ}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    11. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{cos }{\\O}&=&\\dfrac{3}{5} \\\\ \\\\\r\n{\\O}&=&\\text{cos }^{-1}\\left(\\dfrac{3}{5}\\right) \\\\ \\\\\r\n{\\O}&=&53.1\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n3^2+y^2&=&5^2 \\\\ \\\\\r\ny&=&\\sqrt{5^2-3^2} \\\\ \\\\\r\ny&=&4\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    12. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{cos }24^{\\circ}&=&\\dfrac{25}{z} \\\\ \\\\\r\nz&=&\\dfrac{25}{\\text{cos }24^{\\circ}} \\\\ \\\\\r\nz&=&27.4\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\text{tan }24^{\\circ}&=&\\dfrac{y}{25} \\\\ \\\\\r\ny&=&25\\text{ tan }24^{\\circ} \\\\ \\\\\r\ny&=&11.1\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    13. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{sin }{\\O}&=&\\dfrac{28}{40} \\\\ \\\\\r\n{\\O}&=&\\text{sin }^{-1}\\left(\\dfrac{28}{40}\\right) \\\\ \\\\\r\n{\\O}&=&44.4^{\\circ}\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrl}\r\nz^2+28^2&=&40^2 \\\\ \\\\\r\nz&=&\\sqrt{40^2-28^2} \\\\ \\\\\r\nz&=&28.6\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    14. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{cos }{\\O}&=&\\dfrac{20}{28} \\\\ \\\\\r\n{\\O}&=&\\text{cos }^{-1}\\left(\\dfrac{20}{28}\\right) \\\\ \\\\\r\n{\\O}&=&44.4^{\\circ}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n20^2+y^2&=&28^2 \\\\ \\\\\r\ny&=&\\sqrt{28^2-20^2} \\\\ \\\\\r\ny&=&19.6\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    15. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{sin }{\\O}&=&\\dfrac{8}{12} \\\\ \\\\\r\n{\\O}&=&\\text{sin}^{-1}\\left(\\dfrac{8}{12}\\right) \\\\ \\\\\r\n{\\O}&=&41.8^{\\circ}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}{rrl}\r\ny^2+8^2&=&12^2 \\\\ \\\\\r\ny&=&\\sqrt{12^2-8^2} \\\\ \\\\\r\ny&=&8.9\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    16. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{tan }35^{\\circ}&=&\\dfrac{x}{50} \\\\ \\\\\r\nx&=&50\\text{ tan }35^{\\circ} \\\\ \\\\\r\nx&=&35\r\n\\end{array}\r\n&\\hspace{0.5in}\r\n\\begin{array}{rrl}\r\n\\text{cos }35^{\\circ}&=&\\dfrac{50}{y} \\\\ \\\\\r\ny&=&\\dfrac{50}{\\text{cos }35^{\\circ}} \\\\ \\\\\r\ny&=&61\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
        \n
      1. 0.743145<\/li>\n
      2. 0.484810<\/li>\n
      3. 0.906308<\/li>\n
      4. 0.484810<\/li>\n
      5. 0.194380<\/li>\n
      6. 1.53986<\/li>\n
      7. 0.190810<\/li>\n
      8. 0.544639<\/li>\n
      9. 29\u00b0<\/li>\n
      10. 39\u00b0<\/li>\n
      11. 50\u00b0<\/li>\n
      12. 52\u00b0<\/li>\n
      13. 33.3\u00b0<\/li>\n
      14. 8.9\u00b0<\/li>\n
      15. 41\u00b0<\/li>\n
      16. 81\u00b0<\/li>\n<\/ol>\n

         <\/p>\n

          \n
        1. \"\begin{array}{ll}<\/li>\n
        2. \"\begin{array}{ll}<\/li>\n
        3. \"\begin{array}{ll}<\/li>\n
        4. \"\begin{array}{ll}<\/li>\n
        5. \"\begin{array}{ll}<\/li>\n
        6. \"\begin{array}{ll}<\/li>\n
        7. \"\begin{array}{ll}<\/li>\n
        8. \"\begin{array}{ll}<\/li>\n
        9. \"\begin{array}{ll}<\/li>\n
        10. \"\begin{array}{ll}<\/li>\n
        11. \"\begin{array}{ll}<\/li>\n
        12. \"\begin{array}{ll}<\/li>\n
        13. \"\begin{array}{ll}<\/li>\n
        14. \"\begin{array}{ll}<\/li>\n
        15. \"\begin{array}{ll}<\/li>\n
        16. \"\begin{array}{ll}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":108,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1852","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1852","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1852\/revisions"}],"predecessor-version":[{"id":1856,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1852\/revisions\/1856"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1852\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1852"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1852"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1852"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1852"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}