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# 0 - Extramarks by pengxiang

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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

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
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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