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NCERT Solutions for Exercise 9.1 Class 10 Maths Chapter 9 Some Applications of Trigonometry are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2024-25. Class 10 maths ex 9.1 deal the application of trigonometry and to be specified, cover all the problems and questions related to height and distances in which we will use trigonometry to find the aspects asked.
NCERT solutions for exercise 9.1 Class 10 Maths chapter 9 Some Applications of Trigonometry focuses on using trigonometry to find the angle of depression, angle of elevation and line of sight along with this finding the height or length of an object or the distance between two distant objects. 10th class Maths exercise 9.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Some Applications of Trigonometry Class 10 Chapter 9 Excercise: 9.1
Answer:
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.
Answer:
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)
Answer:
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.
Answer:
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
Answer:
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.
Answer:
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 =
Answer:
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
Answer:
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
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
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.
Answer:
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
Answer:
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.
Answer:
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.
NCERT syllabus Class 10 Maths chapter 9 exercise 1: The questions in exercise 9.1 Class 10 Maths, broadly consist of some basic questions in which we have to find height and distance with the help of the formula of tangent, cosine and sine. NCERT solutions for NCERT book Class 10 Maths exercise 9.1 also consist of questions that are a little bit harder as we have to apply the trigonometric formula twice and also use some basic phenomena of real life such as the shadow of objects. Exercise 9.1 Class 10 Maths covers all types of questions that can be formed height and distance. Students can find here Some applications of Trigonometry Class 10 Notes that are very helpful in quickly revising all important concepts discussed in this chapter.
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The values of all trigonometric functions dependent on the value of the ratio of sides in a right-angled triangle are known as trigonometric ratios.
angle of depression
angle of elevation
line of sight
finding the height or length of an object or the distance between two distant objects
The angle created by the line of sight with the horizontal when it is above the horizontal level is the angle of elevation of an item that we can see.
When we elevate our head to gaze at an object, for example.
The angle formed by the line of sight with the horizontal when it is below the horizontal level is the angle of depression of an item that we can see.
When we drop our head to gaze at an object, for example.
The line of sight is the line which is a line traced from an observer's eye to a point in the item being seen.
Trigonometric ratios can be used to calculate an object's height or length, as well as the distance between two distant objects.
Before the Class 10 Mathematics chapter 9 activity 9.1, there are seven key questions that must be answered.
In the NCERT solutions for the Class 10 Maths chapter 9 exercise, there are 16 problems.
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Hope you get it !
Thanking you
Hello aspirant,
The dates of the CBSE Class 10th and Class 12 exams are February 15–March 13, 2024 and February 15–April 2, 2024, respectively. You may obtain the CBSE exam date sheet 2024 PDF from the official CBSE website, cbse.gov.in.
To get the complete datesheet, you can visit our website by clicking on the link given below.
https://school.careers360.com/boards/cbse/cbse-date-sheet
Thank you
Hope this information helps you.
Hello aspirant,
The paper of class 7th is not issued by respective boards so I can not find it on the board's website. You should definitely try to search for it from the website of your school and can also take advise of your seniors for the same.
You don't need to worry. The class 7th paper will be simple and made by your own school teachers.
Thank you
Hope it helps you.
The eligibility age criteria for class 10th CBSE is 14 years of age. Since your son will be 15 years of age in 2024, he will be eligible to give the exam.
That totally depends on what you are aiming for. The replacement of marks of additional subjects and the main subject is not like you will get the marks of IT on your Hindi section. It runs like when you calculate your total percentage you have got, you can replace your lowest marks of the main subjects from the marks of the additional subject since CBSE schools goes for the best five marks for the calculation of final percentage of the students.
However, for the admission procedures in different schools after 10th, it depends on the schools to consider the percentage of main five subjects or the best five subjects to admit the student in their schools.
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