Question 1 :
The angles of elevation of the top of a vertical tower from points at distance $a$ and $b$ from the base and in the same line with it are complementary. If $a > b$, find the height of the tower.

Question 2 :
The angle of elevation a vertical tower standing inside a triangular at the vertices of the field are each equal to $\theta$. If the length of the sides of the field are $30\ m,\ 50\ m$ and $70\ m$, the height of the tower is:<br/>

Question 3 :
A ladder is placed against tower. If the ladder makes an angle of $30^{\circ}$ with the ground and reaches upto a height of 15 m of the tower; find length of the ladder.

Question 4 :
If the ratio of height of a tower and the length of its shadow on the ground is $\sqrt{3}:1 $, then the angle of elevation of the sun is<br/>

Question 5 :
Each side of square subtends an angle of $60^{o}$ at the top of a tower of $h$ meter height standing in the centre of the square. If $a$ is the length of each side of the square then which of the following is/are correct?<br/>

Question 6 :
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 7 :
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 8 :
$OAB$ 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 9 :
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 10 :
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 $50\ &#160;m$, the observer finds the new angle of elevation as $30^{\circ}$. What is the width of the river ?