{"id":182989,"date":"2025-01-15T09:44:57","date_gmt":"2025-01-15T09:44:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=182989"},"modified":"2025-01-15T09:44:59","modified_gmt":"2025-01-15T09:44:59","slug":"he-bearings-of-the-lines-oa-ob-oc-od-are-3030-%e2%80%b2-14015-%e2%80%b2-22045-%e2%80%b2-and-31030","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/15\/he-bearings-of-the-lines-oa-ob-oc-od-are-3030-%e2%80%b2-14015-%e2%80%b2-22045-%e2%80%b2-and-31030\/","title":{"rendered":"he bearings of the lines OA, OB, OC, OD are 30\u00b030 \u2032, 140\u00b015 \u2032, 220\u00b045 \u2032 and 310\u00b030"},"content":{"rendered":"\n

he bearings of the lines OA, OB, OC, OD are 30\u00b030 \u2032, 140\u00b015 \u2032, 220\u00b045 \u2032 and 310\u00b030 \u2032, respectively. Find the angles \u2220AOB, \u2220BOC and \u2220COD.<\/p>\n\n\n\n

The fore bearings of the lines AB, BC, CD and DE, are 45\u00b030 \u2032 120\u00b015 \u2032, 200\u00b030 \u2032 and 280\u00b045 \u2032, respectively. Find angles \u2220B, \u2220C and \u2220D.<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To solve the given problems, we need to calculate the angles between the lines from the bearings provided, first for the angles \u2220AOB, \u2220BOC, \u2220COD, and then for the angles \u2220B, \u2220C, and \u2220D.<\/p>\n\n\n\n

1. Angles \u2220AOB, \u2220BOC, \u2220COD (from the bearings of OA, OB, OC, and OD)<\/strong>:<\/h3>\n\n\n\n

We are given the following bearings:<\/p>\n\n\n\n

    \n
  • OA: 30\u00b030\u2032<\/li>\n\n\n\n
  • OB: 140\u00b015\u2032<\/li>\n\n\n\n
  • OC: 220\u00b045\u2032<\/li>\n\n\n\n
  • OD: 310\u00b030\u2032<\/li>\n<\/ul>\n\n\n\n

    To find the angles between the lines, we calculate the difference between the bearings of the respective lines:<\/p>\n\n\n\n

    \u2220AOB:<\/h4>\n\n\n\n

    The bearing of line OA is 30\u00b030\u2032, and the bearing of line OB is 140\u00b015\u2032. The angle \u2220AOB is the difference between these two bearings:
    [
    \\text{\u2220AOB} = 140\u00b015\u2032 – 30\u00b030\u2032 = 109\u00b045\u2032
    ]<\/p>\n\n\n\n

    \u2220BOC:<\/h4>\n\n\n\n

    The bearing of line OB is 140\u00b015\u2032, and the bearing of line OC is 220\u00b045\u2032. The angle \u2220BOC is:
    [
    \\text{\u2220BOC} = 220\u00b045\u2032 – 140\u00b015\u2032 = 80\u00b030\u2032
    ]<\/p>\n\n\n\n

    \u2220COD:<\/h4>\n\n\n\n

    The bearing of line OC is 220\u00b045\u2032, and the bearing of line OD is 310\u00b030\u2032. The angle \u2220COD is:
    [
    \\text{\u2220COD} = 310\u00b030\u2032 – 220\u00b045\u2032 = 89\u00b045\u2032
    ]<\/p>\n\n\n\n

    2. Angles \u2220B, \u2220C, and \u2220D (from the fore bearings of lines AB, BC, CD, and DE)<\/strong>:<\/h3>\n\n\n\n

    We are given the following fore bearings:<\/p>\n\n\n\n

      \n
    • AB: 45\u00b030\u2032<\/li>\n\n\n\n
    • BC: 120\u00b015\u2032<\/li>\n\n\n\n
    • CD: 200\u00b030\u2032<\/li>\n\n\n\n
    • DE: 280\u00b045\u2032<\/li>\n<\/ul>\n\n\n\n

      To find the angles at points B, C, and D, we calculate the difference between the respective fore bearings:<\/p>\n\n\n\n

      \u2220B:<\/h4>\n\n\n\n

      The fore bearing of line AB is 45\u00b030\u2032, and the fore bearing of line BC is 120\u00b015\u2032. The angle \u2220B is:
      [
      \\text{\u2220B} = 120\u00b015\u2032 – 45\u00b030\u2032 = 74\u00b045\u2032
      ]<\/p>\n\n\n\n

      \u2220C:<\/h4>\n\n\n\n

      The fore bearing of line BC is 120\u00b015\u2032, and the fore bearing of line CD is 200\u00b030\u2032. The angle \u2220C is:
      [
      \\text{\u2220C} = 200\u00b030\u2032 – 120\u00b015\u2032 = 80\u00b015\u2032
      ]<\/p>\n\n\n\n

      \u2220D:<\/h4>\n\n\n\n

      The fore bearing of line CD is 200\u00b030\u2032, and the fore bearing of line DE is 280\u00b045\u2032. The angle \u2220D is:
      [
      \\text{\u2220D} = 280\u00b045\u2032 – 200\u00b030\u2032 = 80\u00b015\u2032
      ]<\/p>\n\n\n\n

      Summary of Results<\/strong>:<\/h3>\n\n\n\n
        \n
      • \u2220AOB = 109\u00b045\u2032<\/li>\n\n\n\n
      • \u2220BOC = 80\u00b030\u2032<\/li>\n\n\n\n
      • \u2220COD = 89\u00b045\u2032<\/li>\n\n\n\n
      • \u2220B = 74\u00b045\u2032<\/li>\n\n\n\n
      • \u2220C = 80\u00b015\u2032<\/li>\n\n\n\n
      • \u2220D = 80\u00b015\u2032<\/li>\n<\/ul>\n\n\n\n

        Explanation<\/strong>:<\/h3>\n\n\n\n
          \n
        • Bearings are the angles measured clockwise from the north direction.<\/li>\n\n\n\n
        • To find the angle between two lines, we subtract the smaller bearing from the larger bearing.<\/li>\n\n\n\n
        • If the result exceeds 180\u00b0, subtract it from 360\u00b0 to get the smaller angle.<\/li>\n\n\n\n
        • These calculations are based on the assumption that we are using the correct direction for each bearing and ensuring that the angle between the lines is between 0\u00b0 and 180\u00b0.<\/li>\n<\/ul>\n\n\n\n

          This method ensures that we account for the relative positions of the lines accurately.<\/p>\n","protected":false},"excerpt":{"rendered":"

          he bearings of the lines OA, OB, OC, OD are 30\u00b030 \u2032, 140\u00b015 \u2032, 220\u00b045 \u2032 and 310\u00b030 \u2032, respectively. Find the angles \u2220AOB, \u2220BOC and \u2220COD. The fore bearings of the lines AB, BC, CD and DE, are 45\u00b030 \u2032 120\u00b015 \u2032, 200\u00b030 \u2032 and 280\u00b045 \u2032, respectively. Find angles \u2220B, \u2220C and \u2220D. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-182989","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182989","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=182989"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/182989\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=182989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=182989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=182989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}