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0 - Extramarks by pengxiang

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									TO



E-LESSON
DAY’S LESSON
   PRESENTED BY



ASHIM NATH
PGT(MATHS)
J N V HARINAGAR
KARIMGANJ ASSAM
  To Develop Thinking , Analytical , Geometrical
Concept Of Mathematics


   To Appriciate Development Of Mathematics Subject
In Various Fields.


  To Understand Importance Of    Mathematics In Day
To Day Life.
  KNOWLEDGE
                    To acquaint students about the
                    concept of angle of elevation and
                    angle of depression

UNDERSTANDING   To understand the method of
                finding height and distance


APPLICATION       To apply the acquired
                  knowledge to find the height
                  and distance of tower , building
                  , width of river. etc.


  SKILL           To develop skill of drawing the
                  diagram of the problems
  PREVIOUS KNOWLDEGE
  PREVIOUS KNOWLDEGE


 SEE THESE FIGURES
 IN THE BOX FIND THE
 RIGHT ANGLE
 TRIANGLE




THIS IS THE RIGHT
ANGLED TRIANGLE
IN THIS RIGHT TRIANGLE


  B =900
                                         A
AC=h, OPPOSITE TO
RIGHTANGLE B
                                             H
                                              YP
                                                         h


                         PERPENDICULAR
                                                 O
    ACB=θ                                         TU
                                                     N
                                                      SE
                                         p
AB= p      BC=b                                      θ
                                         B                   C
                                             b
                                             BASE
                PANDIT                 BADIRE          PRASAD

Sin θ= P   h    HARI                   HARI                     BOLA

Cos θ= b h
tan θ = p b
                                          H
                                              YP
                                                             h

                   PERPENDICULAR
cosec θ = h p                                      O
                                                    TN
                                                         U
                                                           SE
sec θ = h b                        p
cot θ =b p                                             θ
                                   B
                                              b
                                          BASE
HOW DO YOU MAKE TABLE OF
HOW DO YOU MAKE TABLE OF
TRIGNOMETRIC RATIO ANGLES
TRIGNOMETRIC RATIO ANGLES
     1 WRITE DIGITS, 0 ,1, 2, 3, 4.
     2 DIVIDE EACH DIGIT BY 4.ie
     3 TAKING SQURE ROOT OF EACH SEPERATELY

  ANGLES /RATIOS   0                           60
                          30          45              90
    sinθ           0     1/ 2         1/ 2      3/2   1
   Cosθ                   3/2         1/ 2     1/2
                   1                                  0
    Tanθ           0     1/ 3          1        3     N.D

   Cosecθ          N.D    2                2   2/ 3   1
     secθ          1     2/ 3              2    2     N.D

     cotθ          0        3          1       1/ 3   0
           HORIZONTAL LINE
  THE LINE PASSING THROUGH THE OBSERVER IS
            CALLED HORIZONTAL LINE

 OBJECT IS ABOVE THE          object
 HORIZONTAL LINE




                       HORIZONTAL LINE




                                             OBJECT
                OBJECT ISBELOW THE
OBSERVER        HORIZONTAL LINE
  OBSERVER




                   LI
                     NE
                          OF
                               SI
                                 GH
                                    T

THE LINE JOINING
OBSERVER AND
                                        OBJECT
OBJECT IS CALLED
LINE OF SIGHT
  A tower stands vertically on the
 ground. From a point on the ground
20m away from the foot of the tower
the angle of elevation of the tower is
600. what is the height of the tower?




                     DIAGRAM
                                        SOLUTION

Let AB=h, height of the tower
Given BC= 20m,         C = 60                  A
In right angled triangle ABC
Tanθ=perpendicular / base
Tan 60 = AB / BC
3 =h/20
H = 20 ×. 3
  = 20 ×1.732                     600
   = 3.4640
                   C
                                20m
                                               B
WHEN THE OBJECT WILL BE ABOVE
HORIZONTAL LINE THEN ANGLE
FORMED
 BETWEEN THE LINE OF SIGHT AND
 HORIZONTAL IS CALLED
                                            HT
                                         SIG
                                    OF
                             I NE
                            L




                 HORIZONTAL LINE
ANGLE OF ELEVATION
 ANGLE OF ELEVATION

              LINE OF SIGHT




              HORIZONTAL LINE
                                             WHEN THE
                                     OBJECT WILL BE
                                                 ABOVE
                                           HORIZONTAL
                                             LINE THEN
                                                 ANGLE
            HORIZONTAL LINE                    FORMED
                                         BETWEEN THE
                                         LINE OF SIGHT
                    AN
                       GLE                         AND
LI
                           OF
                              DPR       HORIZONTAL IS
  NE                              ESS           CALLED
       OF                             I
                                     ON
            SI
               GHT
      A flag staff stands on the top of a 5m high tower .
      From a point on the ground , the angle of elevation at
      the top of the flag staff is 600 and from the same point
      , the angle of elevation of the top of the tower is 450 .
      Find the length of the flag staff.
                                                            A
            SOLUTION


                                                                         H
GIVEN BC=5m,
heightof tower.                                                 C
letAC=H be the height
of the tower

                                                                    5m
   ADB=60   0
                                                600
                                         450
   CDB=450                                                  B
                                   D
CONTINUE




  Tanθ= p / b
  In      CBD,
  Tan450=BC/ BD
  1=5 / BD
  BD= 5
  In      ABD,
  Tan 600 =AB/ BD
  3 = (AC+ BC)/ BD
  3 = (H+5) /5
  H = 5 ( 3 – 1)
       QUESTION

                                 D

   From a point on the
  ground 40m, from the
   foot of a tower , the
angle of elevation to the
            top
 Of the tower is 300 the             C
         angle of
the elevation to the top
           of the
  water tank On the top
 of the tower is 450.find
 the height of the tower
            and          A   B
 the depth of the tank?
QUESTION

   As observed from the top
   of 150m tall light house
   the angles of depression
   of two ships approaching
   are 300 and 450. if one ship
   is directly behind the
   other, find the distance
   between the two ships.
        BACK
                               LIGHT HOUSE
         45   0
                   30      0




                                             150


45   0            30   0
    Problems with diagram


A bridge across a river makes
an angle of 450 with the river
bank if the length of the bridge
across the river is 150m, what
is the width of the river ?
DIAGR AM OF
       OBLEM
THE PR         150 m



                   45 0
v Atree breaks due to the strom and the
broken part bends so that the top of the tree
touches the ground making an angle of 30 0
with the ground .the distance from the foot of
the tree to the point where the top touches
the ground is 10m . Find the height of the
tree?
vA Tower stands vertically on the ground.
From a point on the ground, 20m away from
the foot of the tower, the angle of the top of
the tower is 60. what is the height of the
tower ?
vThe shadow of a tower ,standing on level
ground, is found to be 45 m longer than when
sun’s altitude is 30 0 than it was at 60 0. find
the height of the tower?

								
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