NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry This is an application chapter of the previous chapter. In this particular chapter, we will study some ways in which trigonometry is used in our daily life. Solutions of NCERT class 10 maths chapter 9 Some Applications of Trigonometry has covered the detailed explanation to each and every question. In the previous class, you have studied trigonometric ratios. Trigonometry is used in navigation, geography, construction of maps, determining the position of an island, etc. In this chapter, we will learn how trigonometry is used for finding the distances and heights and various objects, without actually measuring them. Trigonometry is one of the most ancient topics studied by scholars all over the world. In this chapter, there is only one exercise with 16 questions, based on the practical application of trigonometry. CBSE NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry are designed by the subject experts to help students in their preparation of board exams. This chapter introduces new terms like the line of sight, angle of depression and angle of elevation. NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry will give you assistance while practicing the questions of the practice exercises including optional exercise. Let's understand a few terms used in this chapter through the diagram.
The line of sight It is an imaginary line drawn from the observer's eye to the object viewed by the observer.
The angle of elevation The angle of elevation of an object viewed by an observer, is the angle formed by the line of sight with the horizontal level when the object is above the horizontal level,
The angle of depression The angle of depression of an object viewed by an observer, is the angle formed by the line of sight with the horizontal level when the object is below the horizontal level.
Along with this particular chapter, NCERT solutions are available subject wise and chapter wise. If you want to go through them then click on the link given.
Given that,
The length of the rope (AC) = 20 m. and
Let the height of the pole (AB) be
So, in the right triangle
By using the Sin rule
m.
Hence the height of the pole is 10 m.
Suppose DB is a tree and the AD is the broken height of the tree which touches the ground at C.
GIven that,
, BC = 8 m
let AB = m and AD = m
So, AD+AB = DB =
In right angle triangle ,
So, the value of =
Similarily,
the value of is
So, the total height of the tree is
= 8 (1.732) = 13.856 m (approx)
Suppose m is the length of slides for children below 5 years and the length of slides for elders children be m.
Given that,
AF = 1.5 m, BC = 3 m, and
In triangle EAF,
The value of is 3 m.
Similarily in CDB,
the value of is = 2(1.732) = 3.468
Hence the length of the slide for children below 5 yrs. is 3 m and for the elder children is 3.468 m.
Let the height of the tower AB is and the angle of elevation from the ground at point C is
According to question,
In the right triangle ,
the value of is = 10(1.732) = 17.32 m
Thus the height of the tower is 17.32 m
A
Given that,
The length of AB = 60 m and the inclination of the string with the ground at point C is .
Let the length of the string AC be .
According to question,
In right triangle CBA,
The value of length of the string () is = 40(1.732) = 69.28 m
Hence the length of the string is 69.28 m.
Given that,
The height of the tallboy (DC) is 1.5 m and the height of the building (AB) is 30 m.
and
According to question,
In right triangle AFD,
So, DF =
In right angle triangle ,
EF =
So, distance walked by the boy towards the building = DF  EF =
Suppose BC = is the height of transmission tower and the AB be the height of the building and AD is the distance between the building and the observer point (D).
We have,
AB = 20 m, BC = m and AD = m
and
According to question,
In triangle BDA,
So, = 20 m
Again,
In triangle CAD,
Answer the height of the tower is 14.64 m
Let the height of the pedestal be m. and the height of the statue is 1.6 m.
the angle of elevation of the top of the statue and top of the pedestal is( )and( ) respectively.
Now,
In triangle ,
therefore, BC = m
In triangle ,
the value of is m
Hence the height of the pedestal is m
It is given that, the height of the tower (AB) is 50 m. and
Let the height of the building be m
According to question,
In triangle PBQ,
.......................(i)
In triangle ABQ,
.........................(ii)
On equating the eq(i) and (ii) we get,
therefore, = 50/3 = 16.66 m = height of the building.
Given that,
The height of both poles are equal DC = AB. The angle of elevation of of the top of the poles are and resp.
Let the height of the poles be m and CE = and BE = 80 
According to question,
In triangle DEC,
..............(i)
In triangle AEB,
..................(ii)
On equating eq (i) and eq (ii), we get
m
So, = 60 m
Hence the height of both poles is ()m and the position of the point is at 60 m from the pole CD and 20 m from the pole AB.
Suppose the is the height of the tower AB and BC = m
It is given that, the width of CD is 20 m,
According to question,
In triangle ,
............(i)
In triangle ACB,
.............(ii)
On equating eq (i) and (ii) we get:
from here we can calculate the value of and the width of the canal is 10 m.
Let the height of the cable tower be (AB = )m
Given,
The height of the building is 7 m and angle of elevation of the top of the tower , angle of depression of its foot .
According to question,
In triangle ,
since DB = CE = 7 m
In triangle ,
Thus, the total height of the tower equal to
Given that,
The height of the lighthouse (AB) is 75 m from the sea level. And the angle of depression of two different ships are and respectively
Let the distance between both the ships be m.
According to question,
In triangle ,
.............(i)
In triangle ,
.............(ii)
From equation (i) and (ii) we get;
Hence, the distance between the two ships is approx 55 m.
Given that,
The height of the girl is 1.2 m. The height of the balloon from the ground is 88.2 m and the angle of elevation of the balloon from the eye of the girl at any instant is () and after some time .
Let the distance travelled by the balloon from position A to position D during the interval.
AB = ED = 88.2  1.2 =87 m
Now, In triangle ,
In triangle ,
Thus, distance traveled by the balloon from position A to D
m
Let be the height of the tower (DC) and the speed of the car be . Therefore, the distance (AB)covered by the car in 6 seconds is 6 m. Let time required to reach the foot of the tower. So, BC =
According to question,
In triangle ,
..........................(i)
In triangle ,
...................(ii)
Put the value of in equation (i) we get,
Hence, from point B car take 3 sec to reach the foot of the tower.
Let the height of the tower be m.
we have PB = 4m and QB = 9 m
Suppose , so
According to question,
In triangle ,
..............(i)
In triangle ,
.....................(ii)
multiply the equation (i) and (ii), we get
Hence the height of the tower is 6 m.
Chapter No. 
Chapter Name 
Chapter 1 
CBSE NCERT solutions for class 10 maths chapter 1 Real Numbers 
Chapter 2 

Chapter 3 
Solutions of NCERT class 10 maths chapter 3 Pair of Linear Equations in Two Variables 
Chapter 4 
CBSE NCERT solutions for class 10 maths chapter 4 Quadratic Equations 
Chapter 5 
NCERT solutions for class 10 chapter 5 Arithmetic Progressions 
Chapter 6 

Chapter 7 
CBSE NCERT solutions for class 10 maths chapter 7 Coordinate Geometry 
Chapter 8 
NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry 
Chapter 9 
NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry 
Chapter 10 

Chapter 11 

Chapter 12 
Solutions of NCERT class 10 chapter maths chapter 12 Areas Related to Circles 
Chapter 13 
CBSE NCERT solutions class 10 maths chapter 13 Surface Areas and Volumes 
Chapter 14 

Chapter 15 
Before coming to this chapter, please ensure that you have completed the previous chapter.
Read the conceptual theory given in the NCERT textbook and have a look over some examples present in the textbook.
Once you complete the above points then you can jump to the practice exercises available in the NCERT textbook.
While practicing the questions in practice exercises, you can use NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry.
When you have done the practice exercise then the best thing to make your concepts strong is the last 5 year papers.
Keep working hard & happy learning!
11. A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joing this point to the foot of the tower, the angle of elevation of the top of the tower is 30° (see Fig. 9.12). Find the height of the tower and the width of the canal.
3. A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
5. 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.