The document discusses trigonometry and its uses in navigation, measuring heights and distances, and astronomical studies. It provides examples of trigonometric ratios like sine, cosine, and tangent for common angles. It then explains concepts like line of sight, angle of elevation and depression. It gives two word problems as examples - one calculating the height of a building given the observer's distance and angle of elevation, and another calculating the height a bird is flying given the angle of depression and distance to an object on the ground.

1.  DONE BY
 SAHANA AND PRIYA
 X-F

2.  Trigonometry is a branch of mathematics
that studies triangles and the
relationships between their sides and the
angles between these sides.

3. Trigonometry describe relationships and
have applicability to cyclical
phenomena, such as waves. It is used
extensively for astronomical studies and
practical art of surveying. It is used in
navigation,measuring heights and
distances.

4. I never knew
that they are
so many uses
for
trigonometry

5.  sin 30 =1/2 tan30=1/ 3
sin 45=1/ 2 tan45=1
sin 60=3/2 tan60= 3
cos30= 3/2
cos45=1/ 2
cos60=1/2

7.  The line of sight is the line drawn from
the eye of an observer to the point
in the object viewed by the
observer.
Horizontal level

8.  The angle of elevation of an object
viewed,is the angle formed by the
line of sight with the horizontal when
it is above the horizontal level.
Horizontal level

9.  The angle of depression of an object
viewed,us the angle formed by the line
of sight with the horizontal when it is
below the horizontal level.
Horizontal level

10.  An observer 1.5m tall is 28.5 m away from
a building.the angle of elevation of the
top of the building from its eyes is
45.what is the height of the building?

11. A
D
E
Horizontal level
1.5 m
B
C

12. Here,AB is the tower ,CD is the observer and
angle ADE is the angle of elevation. In this
case ADE is a triangle,right-angled at E and
we are required to find the height of the
tower .
* AB=AE+BE=AE+1.5
* DE=CB=28.5m
Now, tan45=AE/DE
i.e., 1=AE/28.5
Therefore , AE=28.5m
So,the height of the tower(AB)=(28.5+1.5)m
=30m

13.  Tweety is flying at a certain height above
the ground. suddenly she spots
something peculiar on the ground. She
bends her head forming an angle of
45.the object is placed 20m on the
ground level. Find the height at which
tweety is flying.

14. D A
45
45
C
B

15.  Here, AB is the height at which tweety is flying
BC is the ground level .Angle DAC is the angle
of depression .AC is the line of sight .Angle
ACB=45.
 tan45=opp/adj
 =AB/CB
 1 =AB/20
 Therefore AB=20m
So, height at which tweety is flying =20m

16. !!!THANK YOU!!!