Maths ppt on some applications of trignometry
-
Upload
harsh-mahajan -
Category
Business
-
view
135 -
download
5
description
Transcript of Maths ppt on some applications of trignometry
![Page 1: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/1.jpg)
Some Applications
on Trignometry
![Page 2: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/2.jpg)
What is Trignometry? Trigonometry is a branch
of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
![Page 3: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/3.jpg)
In this topic we shall make use of Trignometric Ratios to find the
height of a tree,a tower,a water tank,width of a river,distance of
ship from lighthouse etc.
![Page 4: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/4.jpg)
Line of Sight We observe generally that children
usually look up to see an aeroplane when it passes overhead.This line joining their
eye to the plane,while looking up is called Line of sight
![Page 5: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/5.jpg)
Line of Sight
Line of Sight
Horizontal
![Page 6: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/6.jpg)
Angle of Elevation The angle which the line of sight makes with a horizontal line drawn away from their eyes is called the
angle of Elevation of aeroplane from them.
![Page 7: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/7.jpg)
Line of Sight
Horizontal
Angel of Elevation
Angel of Elevation
![Page 8: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/8.jpg)
Angel of Depression If the pilot of the aeroplane looks
downwards at any object on the ground then the Angle between his
line of sight and horizontal line drawn away from his eyes is called
Angel of Depression
![Page 9: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/9.jpg)
Angle of Depression
Line of Sight
Horizontal
Angel of Depression
![Page 10: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/10.jpg)
Trignometric Ratios
![Page 11: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/11.jpg)
Now let us Solve some problem
related toHeight and
Distance
![Page 12: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/12.jpg)
The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the
foot of the tower is 30°. Find the height of the tower.
Let AB be the tower and the angle of elevation from point C (on ground) is30°.In ΔABC,
.
Therefore, the height of the tower is
![Page 13: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/13.jpg)
A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the
ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °.
Sol:- It can be observed from the figure that AB is the pole. In ΔABC,
Therefore, the height of the pole is 10 m.
![Page 14: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/14.jpg)
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the
ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in
the string.
Let K be the kite and the string is tied to point P on the ground.In ΔKLP,
.
Hence, the length of the string is
![Page 15: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/15.jpg)
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30 °
with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of
the tree.
Let AC was the original tree. Due to storm, it was broken into two parts. The broken part
In
,
is making 30° with the ground.
![Page 16: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/16.jpg)
Height of tree =
.
+ BC
Hence, the height of the tree is
![Page 17: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/17.jpg)
The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m. from the base of the tower and in the same straight line with it are complementary. Prove that the height of the
tower is 6 m.
Let AQ be the tower and R, S are the points 4m, 9m away from the base of the tower respectively.The angles are complementary. Therefore, if one angle is θ, the other will be 90 − θ.In ΔAQR,
![Page 18: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/18.jpg)
In ΔAQS,
On multiplying equations (i) and (ii), we obtain
However, height cannot be negative.Therefore, the height of the tower is 6 m.
![Page 19: Maths ppt on some applications of trignometry](https://reader035.fdocuments.us/reader035/viewer/2022081717/54c834cd4a7959e8628b464d/html5/thumbnails/19.jpg)