Question 1 :
What is the length of the chord of a unit circle which substends an angle $\theta$ at the centre ?
Question 2 :
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 3 :
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 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 :
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 6 :
A ladder is placed against a vertical tower. If the ladder makes an angle of $\displaystyle 30^{\circ}$ with the ground and reaches up to a height of $15\ m$ of the tower; find length of the ladder in cm.
Question 7 :
A ladder rests against a wall at an angle $\alpha$ to the horizontal. Its foot is pulled away from the wall through a distance $a$ slides a distance $b$ down the wall making an angle $\beta$ with the horizontal. Choose the correct option-
Question 8 :
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 9 :
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 10 :
A vertical pole subtends an angle $\tan^{-1}\left (\dfrac {1}{2}\right )$ at a point P on the ground. If the angles subtended by the upper half and the lower half of the pole at P are respectively $\alpha$ and $\beta$ then $(\tan \alpha, \tan \beta) =$
Question 11 :
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 12 :
The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of $30^o$ with horizontal, then the length of the wire is
Question 14 :
$AB$ is a vertical pole with $B$ at the ground level and $A$ at the top. A man finds that the angle of elevation of the point A from a certain point $C$ on the ground is $60^{{o}}$. He moves away from the pole along the line $BC$ to a point $D$ such that $CD=7$ m. From $D$ the angle of elevation of the point $A$ is $45^{{o}}$. Then the height of the pole is <br/>
Question 15 :
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 16 :
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 17 :
The angle of elevation of a jet plane from a point A on the ground is${ 60 }^{ 0 }$. After a flight of 15 seconds, the angle of elevation changes to${ 30 }^{ 0 }$. If the plane at a constant height of$1500\sqrt { 3 } m$, then the speed of jet plane is :
Question 18 :
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 19 :
Two poles of equal heights are standing opposite each other on either side of the road which is $80$ m wide. From the points between them on the road, the  elevation of the top of the poles are ${60^ \circ }$ and ${30^ \circ }$ respectively. Find the height of the poles.
Question 20 :
From the top of a tower $80$ metres high, the angles of depression of two points $P$ and $Q$ in the same vertical plane with the tower are $45^{0}$ and $75^{0}$ respectively, $PQ=$<br>
Question 21 :
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 22 :
$A$ flag staff stands upon the top of a building. $A$t a distance of 40 $m$. the angles of elevation of the tops of the flag staff and building are $60^{ }$ and $30^{0}$ then the height of the flag staff in metres is<br/>
Question 23 :
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 24 :
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 25 :
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 26 :
If the given object is above the level of the observer, then the angle by which the observer raises his head is called _____.
Question 27 :
The angles of elevation of an artificial satellite measured from two earth stations are $30^0$ and $40^0$ respectively. If the distance between the earth stations is 4000 km, then the height of the satellite is
Question 28 :
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 29 :
<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 31 :
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 32 :
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 33 :
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 34 :
From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be $\alpha $ and $\beta $ where $\alpha >\beta $.The height of the tower is $130\ m,$ $\alpha =60^o\: and\: \beta =30^o$.<br/>The distance of the extreme object from the top of the tower is<br/>
Question 35 :
the altitude of the sun when the length of the shadow is $7\sqrt 3m$.
Question 36 :
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 37 :
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 38 :
 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 39 :
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 40 :
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 41 :
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 42 :
$OAB$ 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 43 :
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 44 :
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 45 :
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.
