{"id":1554,"date":"2023-09-29T10:22:15","date_gmt":"2023-09-29T10:22:15","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=1554"},"modified":"2023-09-29T10:22:50","modified_gmt":"2023-09-29T10:22:50","slug":"week-9-and-10-jss-3-second-term-mathematics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-9-and-10-jss-3-second-term-mathematics-notes\/","title":{"rendered":"Week 9 and 10 – Jss 3 Second Term Mathematics Notes"},"content":{"rendered":"

WEEK NINE
\n<\/strong>APPLICATION OF TRIGONOMETRIC RATIOS
\n<\/strong>Examples: a ladder of 10m is placed against a vertical wall such that the angle between the ladder and the horizontal ground is 30o<\/sup><\/p>\n

    \n
  1. \n
    Calculate the distance up the wall the ladder reaches\n<\/div>\n

    Solution
    \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Sin 30o<\/sup> =
    \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0X = 10 x sin 30o<\/sup>
    \n\t\t\t\t\"\"\/\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0X = 5m\n<\/li>\n<\/ol>\n

    \u00a0
    \n\u00a0
    \n\u00a0
    \n\u00a0
    \n\u00a0Exercise
    \nIn a circle, point O is the centre AB is a chord with length 16cm. The radius of the circle is 10cm calculate <\/p>\n

      \n
    1. \n
      The angle A\u00d4B<\/strong>\n\t\t\t\t<\/div>\n<\/li>\n
    2. \n
      The vertical line from the centre to the line AB\n<\/div>\n<\/li>\n<\/ol>\n

      ANGLE OF ELEVATION AND DEPRESSION
      \n<\/strong>Tangent ratio can be used to solve real life problems such as angles of elevation and depression.<\/p>\n

      \u00a0<\/p>\n

        \n
      1. \n
        Angle of Elevation
        \n<\/strong><\/div>\n

        \"\"\/\"\"\/\"\"\/Example: A tower AB is 50m high if the distance from the point C is 80m from A on a level ground find the angle of elevation of B from C\n<\/li>\n<\/ol>\n

        \"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/
        \n\t\t\u00a0\u00a0\u00a0\u00a0<\/p>\n

        \u00a0
        \n\u00a0
        \n\u00a0Let be the angle of elevation of B from C, tan = = 0.6250
        \n = tan-1<\/sup>(0.6250) = 32o<\/sup><\/p>\n

          \n
        1. \n
          Angle of Depression
          \n<\/strong><\/div>\n

          Example: From the top of a cliff of 150m high, John observes that the angle of depression of a boat at sea is 20o<\/sup> calculate the distance of the boat from the foot of the cliff (ignore John’s height)\n<\/li>\n<\/ol>\n

          \"\"\/Solution
          \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Tan 20o<\/sup> =
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0X =
          \n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0X = 412m<\/p>\n

          \u00a0
          \n\u00a0
          \n\u00a0Exercise<\/p>\n

            \n
          1. \n
            The angle of elevation of the top of a building is 35o<\/sup> from a point 55m away on a level ground. Calculate the height of the building\n<\/div>\n<\/li>\n
          2. \n
            From the top of a mountain 150m high a girl notices that the angle of depression of an object at sea is 350o<\/sup>. find the distance of the object from the foot of the mountain (ignore the height of the girl)\n<\/div>\n<\/li>\n<\/ol>\n

            \u00a0\"\"\/\"\"\/\"\"\/Assignment
            \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/<\/p>\n

            \u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

            \u00a0
            \n\u00a0
            \n\u00a0<\/p>\n

              \n
            1. \n
              Calculate angle QRS\n<\/div>\n<\/li>\n
            2. \n
              PR\n<\/div>\n<\/li>\n<\/ol>\n

              \u00a0WEEK 10
              \n<\/strong>BEARINGS
              \n<\/strong>Bearings are measured from the north in the clock wise direction
              \n\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/\"\"\/<\/p>\n

              \u00a0
              \n\u00a0
              \n\u00a0
              \n\u00a0
              \n\u00a0
              \n\u00a0
              \n\u00a0\u00a0\u00a0\u00a0\u00a0
              \n\u00a0
              \n\u00a0\"\"\/
              \n\t\t\"\"\/\"\"\/Examples of bearings using three digits<\/p>\n

                \n
              1. \n
                \"\"\/\"\"\/\"\"\/\"\"\/The bearing of point A from B is 090o<\/sup>\n\t\t\t\t<\/div>\n<\/li>\n<\/ol>\n

                \u00a0
                \n\u00a0
                \n\u00a0
                \n\u00a0
                \n\u00a0
                \n\u00a0
                \n\u00a0
                \n\u00a0\"\"\/\"\"\/<\/p>\n

                  \n
                1. \n
                  \"\"\/\"\"\/\"\"\/\"\"\/The bearing of point P from Q is 210o<\/sup>\n\t\t\t\t<\/div>\n<\/li>\n<\/ol>\n

                  \u00a0
                  \n\u00a0
                  \n\u00a0
                  \n\u00a0Exercise
                  \n<\/strong>Point P and Q are respectively 30km North and 20km west of point R. Work out the bearing of Q from P.
                  \nAssignment
                  \n<\/strong>From point P Wisdom cycles 18km north to point Q, then east to point R. If the bearing of R from p is 065o<\/sup>. What is the distance from Q to R.?<\/p>\n","protected":false},"excerpt":{"rendered":"

                  WEEK NINE APPLICATION OF TRIGONOMETRIC RATIOS Examples: a ladder of 10m is placed against a…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,142],"tags":[],"class_list":["post-1554","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-jss3-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1554","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=1554"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1554\/revisions"}],"predecessor-version":[{"id":1555,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1554\/revisions\/1555"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=1554"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=1554"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=1554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}