Question 1 :
What is the length of the chord of a unit circle which substends an angle $\theta$ at the centre ?
Question 2 :
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 3 :
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 4 :
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 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 :
<br>On the level ground the angle of elevation of the top of a tower is $30^{0 }$ On moving 20 metres nearer tower, the angle of elevation is found to be $60^{0}$ The height of the towerin metres is<br>
Question 7 :
 A person walking along a straight road towards a hill observes at two points distance  $\sqrt{3}$ km, the angle of elevation of the hill to be $30^{0}$ and $60^{0}$. The height of the hill is   
Question 8 :
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 9 :
A tree breaks due to storm and the broken part bends so that the top of the trees touches the ground making an angle ${30}^{o}$ with ground. The distance between the foot of the tree to the point where the top touches the ground is $8m$. Find the height of the tree.
Question 10 :
A man observes the elevation of a balloon to be $30^{0}$ at a point $A$. He then walks towards the balloon and at a certain place $B$, find the elevation to be $60^{0}$. He further walks in the direction of the balloon and finds it to be directly over him at a height of $\dfrac12\ km$, then $AB=$<br/>
Question 11 :
The ladder resting against a vertical wall is inclined at an angle of ${30}^{o}$ to the ground. The foot of the ladder is $7.5m$ from the wall. Find the length of the ladder.
Question 12 :
A $25\ m$ long ladder is placed against a vertical wall such that the foot of the ladder is $7\ m$ from the feet of the wall. If the top of the ladder slides down by $4\ cm$, by how much distance will the foot of the ladder slide ?
Question 13 :
The angle of elevation of the top of tower from the top and bottom of a building h meter high are$\displaystyle \alpha $ and$\displaystyle \beta $ then the height of tower is
Question 14 :
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 15 :
The shadow of a tower on a level plane is found to be $60$ metres longer when the sun's altitude is $30^{0}$ than that when it is $45^{0 }$. The height of the tower in metres is<br/>
Question 16 :
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 17 :
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 18 :
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 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 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 21 :
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 22 :
$OAB$ 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 23 :
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
