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.

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:

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

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

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,

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

Then from figure:

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,

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.

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:

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,

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:

Answer:  (B)

Explanation: Observe the figure,

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.

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:

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:

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,

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.

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

In right triangle CEB

Important Link

Quick Revision Notes : Some Applications of Trigonometry

NCERT Solution : Some Applications of Trigonometry

MCQs: Some Applications of Trigonometry

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