Question 1 :
A man in a boat rowing away from a light-house $100m$ high, takes $2$ minutes to change the angle of elevation of the top of the light-house form ${60}^{o}$ to ${45}^{o}$. Find the speed of the boat.

Question 2 :
Two flagstaffs stand on a horizontal plane. A and B are two points on the line joining their feet and between them. The angles of elevation of the tops of the flagstaff as seen from A are 30$^o$ and 60$^o$ and as seen from B are 60$^o$ and 45$^o$. If AB is 30 m, the distance between the flagstaffs in metres is

Question 3 :
$OAB$ is a triangle in the horizontal plane through the foot $P$ of the tower at the middle point of the side $OB$ of the triangle. If $OA=2\ m,\ OB=6\ m,\ AB=5\ m$ and $\angle AOB$ is equal to the angle subtended by the tower at $A$ then the height of the tower is:

Question 4 :
A man on the deck of a ship is $12m$ above water level. he observes that the angle of elevation, of the top of a cliff is ${45}^{o}$ and the angle of depression of its base is ${30}^{o}$. Calculate the distance of the cliff from the ship and the height of the cliff.

Question 5 :
The angle of elevation from a point on the bank of a river to the top of a temple on the other bank is $45^o$. Retreating $50\  m$, the observer finds the new angle of elevation as $30^{\circ}$. What is the width of the river ?

Question 6 :
The angle of elevation of a Jet fighter from a point $A$ on the ground is ${60}^{o}$. After $10$ seconds flight, the angle of elevation changes to ${30}^{o}$. If the Jet is flying at a speed of $432km/hour$, find the height at which the jet is flying.

Question 7 :
On the same side of a tower, two objects are located. When observed from the top of the tower, their angles of depression are $45^o$ and $60^o$. If the height of the tower is $50\sqrt 3$, then the distance between the objects is

Question 8 :
Horizontal distance between two pillars of different height is 60 m. it was observed that the angular elevation form form the top of the shorter pillar to the top of the taller pillar is$\displaystyle 45^{\circ}$ if the height of taller pillar is 130 m, the height of the shorter pillar