Exercise :: Height and Distance  General Questions
 Height and Distance  Important Formulas
 Height and Distance  General Questions
1.  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: 

Answer: Option C Explanation: Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, ACB = 30° and ADB = 45°.

2.  A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60°. What is the distance between the base of the tower and the point P? 

Answer: Option D Explanation: One of AB, AD and CD must have given. So, the data is inadequate. 
3.  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: 

Answer: Option D Explanation: Let AB be the wall and BC be the ladder. Then, ACB = 60° and AC = 4.6 m.

4.  An observer 1.6 m tall is 203 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is: 

Answer: Option A Explanation: Let AB be the observer and CD be the tower. Draw BE CD. Then, CE = AB = 1.6 m, BE = AC = 203 m.
CD = CE + DE = (1.6 + 20) m = 21.6 m. 
5.  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: 

Answer: Option C Explanation: Let AB be the tower. Then, APB = 30° and AB = 100 m.
