Question 1 :
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 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 :
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 4 :
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 5 :
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&#160;

Question 6 :
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 7 :
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 8 :
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 9 :
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 10 :
A boat is rowed away from a cliff $150$ m high At the top of the the cliff the angle of depression of the boat change from&#160;$\displaystyle 60^{0}$ to&#160;$\displaystyle 45^{0}$ in $2.5$ minutes The speed of the boat (in m/sec) is

Question 11 :
If the given object is above the level of the observer, then the angle by which the observer raises his head is called _____.

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 13 :
$A$ 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 14 :
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 15 :
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 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 $50\ &#160;m$, the observer finds the new angle of elevation as $30^{\circ}$. What is the width of the river ?

Question 17 :
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 18 :
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 19 :
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.