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Trigonometry is used in real life situations where we want to find angles or distances. For example, in measuring the height of a tall building or a mountain, we can use trigonometric ratios like sine, cosine, or tangent. It’s also used in navigation, which includes locating the location of a ship or a plane. Concepts like line of sight, angle of elevation, and angle of depression help us measure things that are far away.
This article on NCERT Class 10 Maths Chapter 9 Solutions of Some Applications of Trigonometry provides clear and step-by-step solutions for exercise problems in NCERT Class 10 maths book. These NCERT Solutions are created by subject experts at Careers360, considering the latest CBSE syllabus, 2025-26. For further reference, students can check NCERT Notes For Class 10 Mathematics Chapter Some Applications of Trigonometry and NCERT Exemplar Solutions For Class 10 Mathematics Chapter Trigonometry.
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 of Depression:
The angle of depression is created between the horizontal line (above the angle) and the line of sight to the object.
Class 10 Maths Chapter 9 Solutions Exercise: 9.1 Page Number: 141-143 Total Questions: 15 |
Answer:
Given that,
The length of the rope (AC) = 20 m. and ∠ACB =30o
Let the height of the pole (AB) be h
So, in the right triangle ΔABC
By using the Sin rule
sinθ=PH=ABAC
sin30o=h20
h=10 m.
Hence, the answer 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,
∠ACB=30o , BC = 8 m
Let AB = x m and AD = y m
So, AD+AB = DB = x+y
In right angle triangle ΔABC ,
tanθ=PB=x8
tan30o=x8=13
So, the value of x = 8/3
Similarly,
cos30o=BCAC=8y
The value of y is 16/3
So, the total height of the tree is-
x+y=243=83
= 8 (1.732) = 13.856 m (approx)
Hence, the answer is 13.856 m (approx)
Answer:
Suppose x m is the length of slides for children below 5 years and the length of slides for elderly children is y m.
Given that,
AF = 1.5 m, BC = 3 m, ∠AEF=30o and ∠BDC=60o
In triangle Δ EAF,
sinθ=AFEF=1.5x
sin30o=1.5x
The value of x is 3 m.
Similarly in Δ CDB,
sin60o=3y
32=3y
The value of y is 23 = 2(1.732) = 3.468
Hence the length of the slide for children below 5 years. is 3 m and for the elder children is 3.468 m.
Answer:
Let the height of the tower AB be h and the angle of elevation from the ground at point C is ∠ACB=30o
According to the question,
In the right triangle ΔABC ,
tanθ=ABBC=h30
tan30o=13=h30
The value of h is 103 = 10(1.732) = 17.32 m
Hence, the answer is 17.32 m.
Given that,
The length of AB = 60 m and the inclination of the string with the ground at point C is ∠ACB=60o.
Let the length of the string AC be l.
According to the question,
In right triangle Δ CBA,
sin60o=ABAC=60l
32=60l
The value of length of the string ( l ) is 403 = 40(1.732) = 69.28 m
Hence, the answer 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.
∠ADF=30o and ∠AEF=60o
According to the question,
In right triangle AFD,
⇒tan30o=AFDF=28.5DF⇒13=28.5DF
So, DF = (28.5)3
In right angle triangle ΔAFE ,
tan60o=AFFE=28.5EF
3=28.5EF
EF = 9.53
So, distance walked by the boy towards the building = DF - EF = 193
Answer:
Suppose BC = h is the height of the transmission tower AB is
the height of the building and AD is the distance between the building and the observer point (D).
We have,
AB = 20 m, BC = h m and AD = x m
∠CDA=60o and ∠BDA=45o
According to the question,
In triangle Δ BDA,
tan45o=ABAD=20x
So, x = 20 m
Again,
In triangle Δ CAD,
⇒tan60o=AB+BCAD=20+h20⇒3=1+h20⇒h=20(3−1)⇒20(0.732)=14.64m
Hence, the answer is 14.64m
Answer:
Let the height of the pedestal be h 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( ∠DCB= 60o )and( ∠ACB= 45o ) respectively.
Now,
In triangle ΔABC ,
tan45o=1=ABBC=hBC
therefore, BC = h m
In triangle ΔCBD ,
⇒tan60o=BDBC=h+1.6h⇒3=1+1.6h
the value of h is 0.8(3+1) m
Hence the height of the pedestal is 0.8(3+1) m
Answer:
It is given that, the height of the tower (AB) is 50 m. ∠AQB=30o and ∠PBQ=60o
Let the height of the building be h m
According to the question,
In triangle PBQ,
tan60o=PQBQ=50BQ
3=50BQBQ=503 .......................(i)
In triangle ABQ,
tan30o=hBQ
BQ=h3 .........................(ii)
On equating the eq(i) and (ii) we get,
503=h3
Therefore, h = 50/3 = 16.66 m = height of the building.
Answer:
Given that,
The height of both poles is equal to DC = AB. The angle of elevation of the top of the poles is ∠DEC=30o and ∠AEB=60o resp.
Let the height of the poles be h m and CE = x and BE = 80 - x
According to the question,
In triangle DEC,
⇒tan30o=DCCE=hx⇒13=hx⇒x=h3 ..............(i)
In triangle AEB,
⇒tan60o=ABBE=h80−x⇒3=h80−x⇒x=80−h3 ..................(ii)
On equating eq (i) and eq (ii), we get
3h=80−h3
h3=20 So, x = 60 m
Hence the height of both poles is ( h=203 )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 h is the height of the tower AB and BC = x m
It is given that, the width of the CD is 20 m,
According to the question,
In triangle ΔADB ,
tan30∘=AB20+x=h20+x⇒13=h20+x⇒20+x=h3⇒x=h3−20
In triangle ACB,
⇒tan60o=hx=3⇒x=h3 .............(ii)
On equating eq (i) and (ii) we get:
h3−20=h3
from here we can calculate the value of h=103=10(1.732)=17.32m and the width of the canal is 10 m.
Answer:
Let the height of the cable tower be (AB = h+7 )m
Given,
The height of the building is 7 m and the angle of elevation of the top of the tower ∠ACE=60o, angle of depression of its foot ∠BCE=45o
According to the question,
In triangle ΔDBC ,
tan45o=CDBD=7BD=1BD=7 m
since DB = CE = 7 m
In triangle ΔACE ,
tan60o=hCE=h7=3∴h=73 m
Thus, the total height of the tower equal to h+7 =7(1+3) m
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 ∠ADB=300 and ∠ACB=450 respectively
Let the distance between both the ships be x m.
According to the question,
In triangle ΔADB ,
tan300=ABBD=75x+y=13
∴x+y=753 .............(i)
In triangle ΔACB ,
tan450=1=75BC=75y
∴y=75 m .............(ii)
From equation (i) and (ii) we get;
x=75(3−1)=75(0.732)
x=54.9≃55 m
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 ( ∠ACB=600 ) and after some time ∠DCE=300.
Let the x distance traveled by the balloon from position A to position D during the interval.
AB = ED = 88.2 - 1.2 =87 m
Now, In triangle ΔBCA ,
tan600=3=ABBC=87BC∴BC=293
In triangle ΔDCE ,
tan300=13=DECE=87CE∴CE=873
Thus, the distance traveled by the balloon from position A to D
=CE−BC=873−293=583 m
Answer:
Let h be the height of the tower (DC) and the speed of the car be x ms−1. Therefore, the distance (AB)covered by the car in 6 seconds is 6 x m. Let t time required to reach the foot of the tower. So, BC = x t
According to the question,
In triangle ΔDAC ,
tan300=13=h6x+xtx(6+t)=h3 ..........................(i)
In triangle ΔBCD ,
tan600=3=hxt∴h=3.xt ...................(ii)
Put the value of h in equation (i) we get,
x(6+t)=(3.3)xt6x+xt=3xt6x=2xt
t=3
Hence, from point B car takes 3 sec to reach the foot of the tower.
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Here is the latest NCERT syllabus which is very useful for students before strategizing their study plan. Also, links to some reference books which are important for further studies.
In this chapter Trigonometry applications class 10 covered following topics-
NCERT Solutions for Class 10 Maths Chapter 9 PDF is provided in this article. you can just click and download it. Also students can download maths class 10 chapter 9 using the official website fo careers360.
Class 10 9th chapter maths include problems related to height and distance which can be solved using the following 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 command these formulas.
In Applications of trigonometry class 10 questions with solutions, the following important formulas should be remembered:
Admit Card Date:03 February,2025 - 04 April,2025
Admit Card Date:07 March,2025 - 04 April,2025
Admit Card Date:10 March,2025 - 05 April,2025
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).
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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.
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