Aakash Repeater Courses
Take Aakash iACST and get instant scholarship on coaching programs.
Trigonometry isn’t just about triangles; it’s about seeing the world through angles and heights. Applications of trigonometry prove that math is the ladder we climb to measure the surrounding heights. In the last chapter, students learned about trigonometric ratios. The NCERT Solutions for Class 10 Maths Chapter 9, Some Applications of Trigonometry, explain the daily uses of trigonometry to students. This chapter mainly deals with the concepts of heights and distances, angles of elevation, angles of depression, and the line of sight.
Don't Miss: Best Courses after 10th | Competitive Exams after 10th
Don't Miss: JEE Main & NEET 2026 Scholarship Test (Class 10): Narayana | Aakash
Trigonometry makes heights and distances easy to measure, demonstrating how math can connect the earth with the sky. The NCERT solutions for Class 10 presented here are based on the revised CBSE syllabus for 2025-26, available from Careers360 subject matter experts who wrote these easy-to-understand solutions and showed a stepwise explanation of each question with connected pictures. For details about the syllabus, revisions, and to download PDF files, refer to this link: NCERT.
NCERT Some Applications of Trigonometry Class 10 Solutions: Exercise 9.1 Total questions: 15 |
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 sine rule
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,
let AB =
So, AD+AB = DB =
In right angle triangle
So, the value of
Similarily,
the value of
So, the total height of the tree is-
= 8 (1.732) = 13.856 m (approx)
Suppose
Given that,
AF = 1.5 m, BC = 3 m,
In triangle
The value of
Similarily in
the value of
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
According to the question,
In the right triangle
the value of
Thus the height of the tower is 17.32 m
Answer:
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 the question,
In right triangle
The value of length of the string (
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.
According to the 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 =
We have,
AB = 20 m, BC =
According to the question,
In triangle
So,
Again,
In triangle
Answer- The height of the tower is 14.64 m
Let the height of the pedestal be
The angle of elevation of the top of the statue and top of the pedestal is(
Now,
In triangle
therefore, BC =
In triangle
the value of
Hence the height of the pedestal is
It is given that, the height of the tower (AB) is 50 m.
Let the height of the building be
According to the question,
In triangle PBQ,
In triangle ABQ,
On equating equations (i) and (ii), we get,
therefore,
Given that,
The height of both poles are equal DC = AB. The angle of elevation of of the top of the poles are
Let the height of the poles be
According to the question,
In triangle DEC,
In triangle AEB,
On equating eq (i) and eq (ii), we get
So,
Hence, the height of both poles is (
Suppose the
It is given that the width of CD is 20 m,
According to the question,
In triangle
In triangle ACB,
On equating equations (i) and (ii), we get:
from here we can calculate the value of
Let the height of the cable tower be (AB =
Given,
The height of the building is 7 m and angle of elevation of the top of the tower
According to the 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 above sea level. And the angle of depression of two different ships are
Let the distance between both the ships be
According to the question,
In triangle
In triangle
From equations (i) and (ii) we get;
Hence, the distance between the two ships is approximately 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 (
Let the
AB = ED = 88.2 - 1.2 =87 m
Now, In triangle
In triangle
Thus, the distance travelled by the balloon from position A to D
Let
According to the question,
In triangle
In triangle
Put the value of
Hence, from point B car takes 3 seconds to reach the foot of the tower.
Let the height of the tower be
we have PB = 4m and QB = 9 m
Suppose
According to question,
In triangle
In triangle
Multiply equations (i) and (ii), we get
Hence, the height of the tower is 6 m.
The topics discussed in the NCERT Solutions for class 10, chapter 9, Some Applications of Trigonometry, are:
Take Aakash iACST and get instant scholarship on coaching programs.
Line of Sight - The Line of Sight is the line formed by our vision as it passes through an item when we look at it.
Horizontal Line - The distance between the observer and the object is measured by a horizontal line.
The angle of Elevation:
The angle formed by the line of sight to the top of the item and the horizontal line is called an angle of elevation.
It is above the horizontal line, i.e., when we gaze up at the item, we make an angle of elevation.
The angle of Depression:
When the spectator must look down to perceive the item, an angle of depression is formed.
When the horizontal line is above the angle, the angle of depression is formed between it and the line of sight.
Case 1:
In this case, we can observe the following:
Height of a tower, hill, or building
Distance of an object from the foot of the tower, hill, or building and sometimes the shadow of it
The angle of elevation or the angle of depression
Any two of the above three parameters will be provided in the question. This type of problem can be solved using the formulas given below.
In the right triangle
Case 2:
In this case, we can deal with different illustrations. One of the commonly solved problems is about the movement of an observer. If the observer moves toward objects like a tower, building, hill, etc., then the angle of elevation increases. The angle of elevation decreases when the observer moves away from the object. Here, the distance moved by the observer can be found using the formula given below:
In the right triangle given below,
Case 3:
There is another case where two different situations happen at the same time. In this case, we get similar triangles with the same angle of elevation or angle of depression. These types of problems can be solved with the help of formulas related to similar triangles.
In the right triangle
Here, triangles
Using Thales' or BPT theorem, we can write the ratio of sides as:
For students' preparation, Careers360 has gathered all Class 10 Maths NCERT solutions here for quick and convenient access.
Also, read,
Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.
Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.
Students can check the latest CBSE syllabus from the following links.
In this chapter, Trigonometry applications class 10 covered the following topics-
This article provides NCERT Solutions for Class 10 Maths Chapter 9 PDF. You can just click and download it. Also, students can download Maths Class 10, chapter 9 using the official website of Careers360.
Class 10, chapter 9 of the math textbook, contains problems on height and distance, solvable using these steps.
The easiest way to understand trigonometric ratios in NCERT solutions class 10th maths chapter 9 is:
Use these class 10 NCERT Maths Chapter 9 solutions to master these formulas.
In Applications of trigonometry class 10 questions with solutions, the following important formulas should be remembered:
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
Take Aakash iACST and get instant scholarship on coaching programs.
This ebook serves as a valuable study guide for NEET 2025 exam.
This e-book offers NEET PYQ and serves as an indispensable NEET study material.
As per latest syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE