Height and Distance Problem with Solutions PDF

Height and Distance Question and Solutions PDF

1. 
   

   The angle of elevation of the sun is 60°. Find the length of the shadow of a man who is 180 cm tall.

1. A. 127.27 cm     
2. B. 103.92 cm        Correct Answer
3. C. 311.77 cm      
4. D. None of these      

2.  

   
   

   Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

1. A. 173 m     
2. B. 200 m      
3. C. 273 m        Correct Answer
4. D. 300 m      

3.  

   
   

   What is the distance between a tower and an observer if the angle of elevation from the observer’s eye to the top of the tower (height = 50 m) is 30°? The observer is 1.5 m tall.

1. A. 84       Correct Answer
2. B. 28      
3. C. 30      
4. D. 90      

4.  

   
   

   The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

1. A. 2.3 m     
2. B. 4.6 m      
3. C. 7.8 m      
4. D. 9.2 m        Correct Answer

5.  

   
   

   Two boats are spotted on the two sides of a light house. If the angle of depression made by both the boats from top of the lighthouse is 30° and 45° and the height of the light house is 125 m then find the distance between the two boats.

1. A. 1     
2. B. 188.56 m      
3. C. 250 m      
4. D. 197.17 m        Correct Answer

6.  

   
   

   From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

1. A. 149 m     
2. B. 156 m      
3. C. 173 m        Correct Answer
4. D. 200 m      

7.  

   
   

   A man standing on the terrace of a building watches a car speeding towards him. If at that particular instant the car is 200 m away from the building makes an angle of depression of 60° with the man’s eye and after 8 seconds the angle of depression is 30°, what is the speed of the car?

1. A. 15 m/s     
2. B. 16.67 m/s        Correct Answer
3. C. 25 m/s      
4. D. Cannot be determined      

8.  

   
   

   A ship is approaching an observation tower. If the time taken by the ship to change the angle of elevation from 30° to 45° is 10 minutes, then find the time the ship will take to cover the remaining distance and reach the observation tower assuming the ship to be travelling at a uniform speed.

1. A. 15 minutes 20 seconds     
2. B. 13 minutes 40 seconds        Correct Answer
3. C. 16 minutes 40 seconds      
4. D. Cannot be determined      

9.  

   
   

   On the two sides of a road are two tall buildings exactly opposite to each other. The height of the taller building is 60 m. If the angle of elevation from the top of the smaller building to the top of the taller one is 30° and the angle of depression from top of the taller building to the foot of the smaller one is 30°, then find the height of the smaller building.

1. A. 45     
2. B. 30      
3. C. 40        Correct Answer
4. D. 20      

10.  

    
    

    Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:

1. A. 300 m     
2. B. 173 m      
3. C. 273 m        Correct Answer
4. D. 200 m      

11.  

    
    

    A tree is cut partially and made to fall on ground. The tree however does not fall completely and is still attached to its cut part. The tree top touches the ground at a point 10m from foot of the tree making an angle of 30°. What is the length of the tree?

1. A. 103 m       Correct Answer
2. B. 10/3 m      
3. C. (2 - 1)/10 m      
4. D. 10/2 m      

12.  

    
    

    Raj stands in a corner of his square farm. Angle of elevation of a scarecrow placed in diagonally opposite corner is 60°. He starts walking backwards in a straight line and after 80ft he realizes that angle of elevation of the scarecrow now is 30°. What is area of the field?

1. A. 1600 sq.ft.     
2. B. 40 sq.ft.      
3. C. 40/2 sq.ft.      
4. D. 800 sq.ft.        Correct Answer

13.  

    
    

    Due to sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?

1. A. 63 ft     
2. B. 72 ft      
3. C. 54 ft        Correct Answer
4. D. 48 ft      

14.  

    
    

    When height of a tree is equal to the length of its shadow, what is the angle of elevation of the sun?

1. A. 30 deg     
2. B. 60 deg      
3. C. 90 deg      
4. D. 45 deg        Correct Answer

15.  

    
    

    A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?

1. A. 50(3 - 1)/ 3 m       Correct Answer
2. B. 503 m      
3. C. 25/3 m      
4. D. None of these      

16.  

    
    

    Two houses are in front of each other. Both have chimneys on their top. The line joining the chimneys makes an angle of 45° with the ground. How far are the houses from each other if one house is 25m and other is 10m in height?

1. A. 18 m     
2. B. 12 m      
3. C. 7.5 m      
4. D. 15 m        Correct Answer

17.  

    
    

    Ramesh and Suresh’s mud forts have heights 8cm and 15 cm. They are 24 cm apart. How far are the fort tops from each other?

1. A. 31 cm     
2. B. 24 cm      
3. C. 25 cm        Correct Answer
4. D. 24.5 cm      

18.  

    
    

    Tree top’s angle of elevation is 30° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60° from the same point. How much did the tree grow?

1. A. 1003 m     
2. B. 2003 m        Correct Answer
3. C. 300(1/3)      
4. D. 200/3 m      

19.  

    
    

    A tree breaks and falls to the ground such that its upper part is still partially attached to its stem. At what height did it break, if the original height of the tree was 24 cm and it makes an angle of 30° with the ground?

1. A. 12 cm     
2. B. 8 cm        Correct Answer
3. C. 9.5 cm      
4. D. 7.5 cm      

20.  

    
    

    Mohan looks at a tree top and the angle made is 45°. He moves 10 cm back and again looks at the tree top but this time angle made is 30°.  How high is the tree top from ground?

1. A. 10/(3+1) cm     
2. B. 203 cm      
3. C. 20 cm      
4. D. 10/(3-1) cm        Correct Answer

21.  

    
    

    There is a tree between houses of A and B. If the tree leans on A’s House, the tree top rests on his window which is 12 m from ground. If the tree leans on B’s House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m, what is distance between A’s and B’s house?

1. A. 21 m       Correct Answer
2. B. 25 m      
3. C. 16 m      
4. D. 12 m      

22.  

    
    

    Angles of elevation of pole are 60° and 45° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?

1. A. height and distance       Correct Answer
2. B. height and speed      
3. C. 3mn units      
4. D. mn units      

23.  

    
    

    Guddi was standing on a road near a mall. She was 1000m away from the mall and able to see the top of the mall from the road in such a way that top of the tree, which is in between her and the mall, was exactly in line of sight with the top of the mall. The tree height is 10m and it is 20m away from Guddi. How tall is the mall?

1. A. 423.5 m     
2. B. 450 m      
3. C. 470 m        Correct Answer
4. D. 495 m      

24.  

    
    

    Rohit while seeing a bird on tree top made 45° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60° angle of elevation. How far was Rohit from the tree initially?

1. A. (2403)/(3-1) ft       Correct Answer
2. B. 240/(3-1) ft      
3. C. 240/3 ft      
4. D. 2403 ft      

25.  

    
    

    There is a tower of 10m between two parallel roads. The angles of depression of the roads from the top of the tower are 30° and 45°.  How far are the roads from each other?

1. A. 27.32 m       Correct Answer
2. B. 29.56 m      
3. C. 203 m      
4. D. 10/3 m      

26.  

    
    

    A and B are standing on ground 50 meters apart. The angles of elevation for these two to the top of a tree are 60° and 30°. What is height of the tree?

1. A. 503 m     
2. B. 25/3 m      
3. C. 253 m        Correct Answer
4. D. 25/(3-1) m