CBSE Class 10th Maths| Applications of Trigonometry MCQ with Answers PDF

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CBSE Class 10th Maths| Applications of Trigonometry MCQ with Answers PDF

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MCQs based on the important concepts and topics of Chapter 9-Applications of Trigonometry of Class 10 Maths NCERT are provided here. All the questions are provided with answers and detailed explanations. Students should practice with all these questions to brush up on their concepts and get prepared to attempt the 1 mark questions appropriately in the CBSE Class 10 Maths Exam 2021-2022.

Check below the solved MCQs from Class 10 Maths Chapter 9 Applications of Trigonometry:

1. If the length of the shadow of a tower is increasing, then the angle of elevation of the sun

(A) is also increasing                      

(B) is decreasing

(C) remains unaffected

(D) Don’t have any relation with length of shadow

Answer: (B)

Explanation: Observe the following figure, Let A represents sun, then as the length of shadow increases from DC to DB , the angle of elevation decreases from 60 to 30.

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

2. The angle of elevation of the top of a tower is 30°. If the height of the tower is doubled, then the angle of elevation of its top will

(A) also get doubled                                                      

(B) will get halved

(C) will be less than 60 degree                   

(D) None of these

Answer: (C)

Explanation: According to Question:

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

Also Check: CBSE Class 10 Science Important MCQs from All Chapters

3. If the height of a tower and the distance of the point of observation from its foot,both, are increased by 10%, then the angle of elevation of its top

(A) increases                                                                                     

(B) decreases

(C) remains unchanged                                                

(D) have no relation.

Answer:  (C)

Explanation: Since          

tan θ = h/x

Where h is height and x is distance from tower,

If both are increased by 10%, then the angle will remain unchanged.

4. A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be

(A) 7.5m                                                                              

(B) 7.7m

(C) 8.5m                                                                              

(D) 8.8m

Answer:  (A)

Explanation: Given that the height of ladder is 15m

Let height of vertical be = h

And the ladder makes an angle of elevation 60° with the wall

In triangle QPR

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

5. An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high.Determine the angle of elevation of the top of the tower from the eye of the observer.

(A) 30°                                                                                                             

(B) 45°

(C) 60°                                                                                                 

(D) 90°

Answer:  B

Explanation: Let the angle of elevation of the tower from the eye of observer be θ.

Given that:

AB = 22m, PQ = 1.5m = MB

QB = PM = 20.5m

AM = AB − MB = 22 − 1.5 = 20.5m

Now in triangle APM

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

6. The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is:

(A) st                                                                                    

(B) s2t2

(C) √st                                                                 

(D) s/t

Answer:  (C)

Explanation: Let the height of tower be h.

Construct figure according to given information as,

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

Also Check: CBSE Class 10 Science Important Questions for Board Exam

7. The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Then the height of tower is:

(A) 20√3                                             

(B) 25√3

(C) 10√3                                             

(D) 30√3

Answer:  (B)

Explanation: Given condition can be represented as follows where SQ is the pole.

Let the height be h and RQ = x m

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

Then from figure:

 CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

8. If a man standing on a platform 3 metres above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is

(A) equal to the angle of depression of its reflection.

(B) double to the angle of depression of its reflection

(C) not equal to the angle of depression of its reflection

(D) information insufficient

Answer:  (C)

Explanation: Observe the figure,

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

We know that if P is a point above the lake at a distance d, then the reflection of the point in the lake would be at the same distance d.

Also the angle of elevation and depression from the surface of the lake is same.

Here the man is standing on a platform 3m above the surface , so its angle of elevation to the cloud and angle of depression to the reflection of the cloud cannot be same.

CBSE Class 10th Board Exam: Important Tips to Finish Maths Paper on Time

9. If a pole 6m high casts a shadow 2√3 m long on the ground, then the sun’s elevation is

(A) 60°                                                                   

(B) 45°

(C) 30°                                                 

(D) 90°

Answer:  (A)

Explanation: According to Question:

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

Therefore,

tan θ = 6/2√3

⇒ tan θ = √3

⇒ tan θ = tan60°

⇒ θ = 60°

10. The angle of elevation of the top of a tower from certain point is 30°. If the observer moves 20 metres towards the tower, the angle of elevation of the top increases by 15°. Find the height of the tower

(A) 10 (√3 + 1)                                

(B) 5√3

(C) 5 (√3 + 1)                                                   

 (D) 10√3

Answer:(A)

Explanation: Since after moving towards the tower the angle of elevation of the top increases by 15°.

Therefore angle becomes 30° + 15° = 45°

Observe the figure,

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

11. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are α and β, respectively. Then the height of the tower is:

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

Answer:  (B)

Explanation: Observe the figure,

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

12. The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60°, then the distance between the two towers is:

(A) 10√3 m                                                                        

(B) 15√3 m

(C) 12√3 m                                                                        

(D) 36 m

Answer:  (A)

Explanation: Observe the figure,

Let the distance between two towers be x m.

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

From figure,

tan60° = 30/x

⇒ √3 = 30/x

⇒ x = 30/√3

⇒ x = 10√3m

13. The angle of elevation of the top of a vertical tower from a point on the ground is60°. From another point 10 m vertically above the first, its angle of elevation is45°. Find the height of the tower.

(A) 5 (√3 + 3) m                                                              

(B) (√3 +3) m

(C) 15 (√3 +3)                                                  

(D) 5√3

Answer:  (A)

Explanation: According to Question:

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

14. A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be A and B respectively. Then the height of the other house is:

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

Answer:  (B)

Explanation: Observe the figure,

Let the height of another house be H m and distance between two houses is x m.

From figure,

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions  

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

15. There are two windows in a house. A window of the house is at a height of 1.5 m above the ground and the other window is 3 m vertically above the lower window. Ram and Shyam are sitting inside the two windows. At an instant, the angle of elevation of a balloon from these windows are observed as 45° and 30° respectively. Find the height of the balloon from the ground.

(A) 7.598m                                                                         

(B) 8.269m

(C) 7.269m                                                                         

(D) 8.598 m

Answer:  (D)

Explanation: Let PQ be the ground level, Ram be sitting at A, Shyam be sitting at B and the balloon be at C from the ground.

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

Then

AP = 1.5m

And

AB = 3m

AP = DQ = 1.5m and BA = ED = 3m

Let the height of balloon from ground be h,

Then CE = (h − 4.5)m

In right triangle ADC

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

In right triangle CEB

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9 Applications of Trigonometry with Detailed Solutions

All the above MCQ questions can also be downloaded in PDF from the following link:

CBSE 10th Maths Exam 2020: Important MCQs from Chapter 9Applications of Trigonometry with Detailed Solutions

 

Also check the following link to get MCQs on other chapters of CBSE Class 10 Maths:

All the MCQs provided by Jagran Josh are only meant to help students identify the important concepts and topics so that they can prepare for their exams in a productive manner to grab the best results in the upcoming board exams.

Important Articles for the Preparation of CBSE Class 10 Maths Exam:

Here we are providing some articles which have been specially created to help students easily prepare for their CBSE Class 10 Maths exam effectively with minimum effort. Links to all such important articles are provided below:

CBSE Class 10 Maths Case Study Questions for All Chapters (MCQ Type)

CBSE Class 10 Maths Important Questions and Answers for Board Exam

CBSE Class 10 Maths Solved Previous Year Question Papers

CBSE Class 10th Maths Chapter-wise Important Formulas, Theorems & Properties

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