Trigonometry Height and Distance Problems Part - 2

1. Shadow of a man is 1/3 times the height of the man. What will be the sun’s angle of elevation?

1. A. 135°     
2. B. 45°      
3. C. 30°      
4. D. 60°        Correct Answer

2.  

   
   

   A 25 m ladder is placed against a vertical wall of a building. The foot of the ladder is 7 m from the base of the building. If the top of the ladder slips 4 m, then the foot of the ladder will slide 

1. A. 5 meter     
2. B. 8 meter        Correct Answer
3. C. 9 meter      
4. D. 15 meter      

3.  

   
   

   The angle of elevation of the top of a tower at a point G on the ground is 30°. On walking 20 m towards the tower the angle of elevation becomes 60°. The height of the tower is equal to

1. A. 10/√3 meter     
2. B. 20 √3 meter      
3. C. 20/√3 meter      
4. D. 10√3 meter        Correct Answer

4.  

   
   

   The angles of elevation of the top of a tower from two points at distances m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then the height of the tower is

1. A. √mn       Correct Answer
2. B. mn      
3. C. m/n      
4. D. None of these      

5.  

   
   

   The angles of elevation of an artificial satellite measured from two earth stations are 30° and 40°, respectively. If the distance between the earth stations is 4000 km, then the height of the satellite is

1. A. 2000 km     
2. B. 6000 km      
3. C. 3464 km         Correct Answer
4. D. 2828 km      

6.  

   
   

   The angle of elevation of the sun when the length of the shadow of a pole is SQRT(3)  times the height of the pole is

1. A. 30°        Correct Answer
2. B. 45°       
3. C. 60°       
4. D. 75°       

7.  

   
   

   The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle 30° with the horizontal, then the length of the wire is

1. A. 12 m       Correct Answer
2. B. 10 m      
3. C. 8 m      
4. D. None of these       

8.  

   
   

   The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the two trees is

1. A. 9 m     
2. B. 11 m      
3. C. 15 m         Correct Answer
4. D. 31 m       

9.  

   
   

   A tree breaks due to storm and the broken part bends so that the top of the tree first touches the ground, making an angle of 30 with the horizontal. The distance from the foot of the tree to the point where the top touches the ground is 10 m. The height of the tree is 

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

10.  

    
    

    A ladder is inclined to a wall making an angle of 30° with it. A man is ascending the ladder at the rate of 2 m/s. How fast is he approaching the wall? 

1. A. 2 m/s     
2. B. 1.5 m/s      
3. C. 1 m/s        Correct Answer
4. D. None of these        

11.  

    
    

    One side of a parallelogram is 12 cm and its area is 60 cm2. If the angle between the adjacent sides is 30°, then its other side is

1. A. 10 cm       Correct Answer
2. B. 8 cm      
3. C. 6 cm      
4. D. 4 cm      

12.  

    
    

    A person walking along a straight road towards a hill observes at two points, Distance km. the angles of elevation of the hill to be 30° and 60'. The height of the hill is

1. A. 3/2 Km       Correct Answer
2. B. √2/√3 Km      
3. C. (√3 + 1)/2 Km      
4. D. √3 Km      

13.  

    
    

    Mr Gidwani's Padyatra Party wanted to go from Gwalior to Bhubaneswar. The walkers travelled 150 km straight and then took a 45° turn towards Varanasi and walked straight for another 120 km. Approximately. how far was the party from the starting point?

1. A. 250 km       Correct Answer
2. B. 90 km      
3. C. 81 km      
4. D. 30 km      

14.  

    
    

     13. A vertical pole PO is standing at the centre O of a square ABCD. If AC subtends an angle of 90° at the point P of the pole, then the angle subtended by a side of the square at the point P is 
    

1. A. 35°     
2. B. 45°        Correct Answer
3. C. 30°      
4. D. 60°      

15.  

    
    

    The angle of elevation of the top of an unfinished tower at a point distant 120 m from its base is 45°. If the elevation of the top at the same point is to be 60°, the tower must be raised to a height

1. A. 120( √3 + 1 ) m     
2. B. 120( √3 - 1 ) m        Correct Answer
3. C. 10( √3 + 1 ) m       
4. D. None Of These      

16.  

    
    

    What is the height of a tower if the angles of elevation of its top from two points x and y at distances of a and b respectively from the base and on the same straight line with the tower arc complementary? 

1. A. √b / a     
2. B. √a / b      
3. C. √ab        Correct Answer
4. D. None of These      

17.  

    
    

    The angle of elevation of an aeroplane from a point on the ground is 45°. After 15 seconds' flight. the elevation changes to 30°. if the aeroplane is flying at a height of 3000 m, the speed of the plane in km/hr is 

1. A. 208.34 Km/hr     
2. B. 306.72 km/hr      
3. C. 402.056 km/hr      
4. D. 527 km/hr        Correct Answer

18.  

    
    

    A vertical lamp post of height 9 m stands at the corner of a rectangular field. The angle of elevation of its top from the farthest corner is 30°, while from another corner it is 45°. The area of the field is

1. A. 9√2 m²       Correct Answer
2. B. 81√2 m²      
3. C. 8√3 m²      
4. D. 9√3 m²