Question 1 :
A kite is flying with the string inclined at$\displaystyle 45^{\circ}$ to the horizontal If the string is straight and 50 m long the height at which the kite is flying is
Question 2 :
Upper part of a vertical tree which is broken over by the winds just touches the ground and makes an angle of$ \displaystyle 30^{\circ} $ with the ground. If the length of the broken part is 20 meters , then the remaining part of the tree is of length
Question 3 :
What is the length of the chord of a unit circle which substends an angle $\theta$ at the centre ?
Question 4 :
If the altitude of the sun is $60^{\circ}$, the height of a tower which casts a shadow of length 30 m is :<br/>
Question 5 :
The angles of elevation of the top of $12$m high tower from two points in opposite directions with it are complementary. If distance of one point from its base is $16$m, then distance of second point from tower's base is?
Question 6 :
The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sun rays meet the ground at$\displaystyle 60^{\circ}$ Find he angle between the sun rays and the ground at the time of longer shadow.
Question 7 :
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 8 :
From the top of a tower $100m$ high ,the angels of depression of the bottom and the top of a building just opposite to it are observed to be ${60^ \circ }$ and ${45^ \circ }$ respectively,then height of the building is 
Question 9 :
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 11 :
Points A and C lie on a straight road and point B lies directly above the road. The angle of elevation from point A to point B is $35^{\circ}$ and the angle of depression from point B to point C is $35^{\circ}$. If the distance from A to C is $20$ miles. The distance between A and B is 
Question 12 :
A man observes the elevation of a tower to be$ \displaystyle 30^{\circ} $. After advancing 11 cm towards it, he finds that the elevation is$ \displaystyle 45^{\circ} $. The height of the tower to the nearest meter is
Question 13 :
The angle of elevation of stationary cloud from a point 25 ml above the lake is $ 15^0$ and the angle of depression of reflection in the lake is $45^0$ .Then the height of the cloud above the level
Question 15 :
Two boats are sailing in the sea on either side of a lighthouse. At a particular time the angles of depression of the two boats, as observed from the top of the lighthouse are 45$^{\circ}$ and 30$^{\circ}$ respectively. If the lighthouse is 100m high, find the distance between the two boats.<br>
Question 16 :
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 17 :
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 18 :
$OAB$ 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 19 :
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
Question 20 :
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.
