aieee-notes_aieee-notes-mathematics_03

							                                                              AIEEE
                                                     and other Entrance Exams
                                                  MATHEMATICS Notes & Key Point
HEIGHTS AND DISTANCES                                                                                         Chapter - 3

1. Introduction
    • Let ' O' be the observer's eye and OX be the horizontal line through O .



   • If the object P is at a higher level than O , then angle POX( = θ) is called the angle of elevation .




   • If the object P is at a lower level than O , then angle POX is called the angle of depression.



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2. Some results that will be useful in solving problems
   In a triangle ABC ,
                                                                                 e   te
                                                                             lin
   • If AD is median, then AB2 + AC 2 = 2 AD 2 + BD 2     (          :/ /on )
                                                                 p
                                                          ht t
                                                      m
                                             d f ro
                                     d   e
                            n    loa                                              A

                         ow
   • If AD is the angle bisector of ∠BAC .then
                       D                                                 c
                                                                                A/2 A/2
                                                                                            b
          BD AB c
            =  =
          DC AC b                                                                     θ
                                                                     B            D              C




   • If a line is perpendicular to a plane, then it is perpendicular to every line lying in that plane .




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