7. Five mark example problems III

1. From the top of a tower \(50 \ m\) high, the angles of depression of the top and bottom of a tree are observed to be \(30^{\circ}\) and \(45^{\circ}\) respectively. Find the height of the tree. (\(\sqrt{3} = 1.732\))

 

Answer:

 

The height of the tree \(=\)  

(Note: Enter the number in the first box and the unit (short form) in the second box.)

 

2. As observed from the top of a \(60 \ m\) high lighthouse from the sea level, the angles of depression of two ships are \(28^{\circ}\) and \(45^{\circ}\). If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (\(tan \ 28^{\circ} = 0.5317\))

 

Answer:

 

The distance between the two ships \(=\)  

(Note: Enter the number in the first box and the unit (short form) in the second box.)

 

3. A man is watching a boat speeding away from the top of a tower. The boat makes an angle of depression of \(60^{\circ}\) with the man's eye when at a distance of \(200 \ m\) from the tower. After \(10\) seconds, the angle of depression becomes \(45^{\circ}\). What is the approximate speed of the boat (in \(km / hr\)), assuming that it is sailing in still water? (\(\sqrt{3} = 1.732\))

 

Answer:

 

The speed of the boat \(=\)  \(km / hr\).