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A balloon is connected to a metrological ground station by a cable of length 215 m inclined at \(60^\circ \)to the horizontal. The height of the balloon from the ground is?
Sin =
A pole 6 m high casts a shadow \(2\sqrt 3 \)m long on the ground, the sun’s elevation is ?
Tan Q=
Q=
The angles of elevation of the top of a tower from two points distant S and t from its foot are complementary. The height of the tower is?
In ABC
Tan Q =
In APC
Tan(90Q)=
Multiplying equation 1 and 2
Tan Q Tan (90Q)=
Tan Q Cot Q=
1=
There is a small island in the middle of a 100 m wide river and a tall tree stands on the stand P and Q are points directly opposite each other on the two banks an din line with the tree. If the angle of elevation of the top of the tree from P and Q are \(30^\circ \)and \(45^\circ \)respectively. The height of the tree is?
In PRS
X=RS cot
X=RS
X=RS……(1)
In RSQ
SQ=RS cot
100x=RS
X=100RS….(2)
From equation 1 and 2
RS=100RS
RS+RS=100
RS=36.63 m
An airplane flying horizontally at a height of \(2500\sqrt 3 \)above the ground is observed to be at an angle of elevation \(60^\circ \)from the ground. After a flight of 25 seconds the angle of elevation is \(30^\circ \). The speed of the plane in m/sec is?
Tan =
X=
Tan =
S=
The upper part of a tree is broken by the wind and makes an angle of \(30^\circ \)with the ground. The distance from the foot of the tree to the point where the top touches the ground is 5 m. the height of the tree is?
In ABC
Tan =
Cos =
Height of the tree is
A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of\(60^\circ \). The height above the ground of the plane is?
Sin =
The shadow of a tower is equal to its height at 10:45 am. The sun’s altitude is?
Tan Q=
The length of AP in the given figure is?
APD=PAB=(alt angles)
Sin =
The value of AE in the given figure
AED=EAB=(alt angles)
In AED
Sin =
From a point on the ground which is 15 m away from the foot of a tower, the angle of elevation is found to be \(60^\circ \). The height of the tower is?
Tan =
A ladder 14 m long rents against a wall. If the foot of the ladder is 7 m from the wall, the angle of elevation is?
Cos Q=
Cos Q=
Q=
In ABC right angled at B, \(\angle \)A=\(30^\circ \)and AC=6cm, the length of BC is?
Sin =
A river is 60 m wide. A tree of unknown height is on one bank. The angle of elevation of the top of the tree from the point exactly opposite to the foot of the tree on the other bank is \(30^\circ \). The height of the tree is?
Tan =
A ladder 15m long reaches the top of a vertical wall .if the ladder makes an angle of \(60^\circ \)with the wall, the height of the wall is?
Cos =
The angle of elevation of a tower from a point on the same level as the foot of the tower is \(30^\circ \). On advancing 150 m towards the foot of the tower, the angle of elevation of the tower becomes \(60^\circ \). The height of the tower is?
Tan
Tan
Substituting the value of x in equation 1 we get ,
150 +
H(–)=150
H=
A vertical tower stands on a horizontal land and is surmounted by a vertical flag staff of height 12 m. at a point on the plane, the angle of elevation of the bottom and the top of the flag staff are \(45^\circ \)and \(60^\circ \). The height of the tower is?
In ABD
Tan
In ADC
Tan =
From 1 and 2
H=
A player siting on the top of a tower of height 40 m observes the angle of depression of a ball lying on the ground is \(60^\circ \). The distance between the foot and the ball is?
CAB=
=
In ABC
In the given figure, BCD is a rectangle in which segments AP and AQ are drawn. The length of AP+AQ is?
In ADQ,
Sin
InABP
Cos =
AP+AQ=180+120
=300 cm
If the length of the shadow of a tower is increasing then the angle of elevation of the sun?
Let prep resents the sun then as the length of shadow increases from QS to QR, the angle of elevation decreases from to .
If the height of the tower and the distance of the point of observation from its foot both are increased by 20%, then the angle of elevation of its top?
Tan Q=
Where h is height and x is distance from tower. If both are increased, then the angle will remain unchanged.
The line drawn from the eye of an observation to the point in the object viewed by the observer is called?
Line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.
The tops of two points of height 20 m and 14 m are connected by a wire. If the wire makes an angle of \(30^\circ \) with the horizontal , then the length of the wire is?
If two towers of heights h1 and h2 subtend angles of \(60^\circ \)and \(30^\circ \)respectively at the midpoint of the line joining their feet, then h1:h2=?
The angle of elevation of the top of a tower from a point 20 m away from its base is \(45^\circ \). The height of the tower is?
A bridge across a river makes an angle of \(45^\circ \)with the river bank. If the length of the bridge across the river is 150 m, what is the width of the river?
In ABC
Sin =
sin
The angle of elevation of the top of a hill at the foot of a tower is \(60^\circ \)and angle of elevation of top at the tower from the foot of a hill is \(30^\circ \). If the tower is 50 m high, the height of the hill is?
In ABC
Cot =
X=h cot ….(1)
In DBC
Cot =
x=50 cot
h=50
A flagstaff stands at the top of a 5 m high tower from a point on the ground, the angle of elevation of the top of the flag staff is \(60^\circ \)and from the same point, the angle of elevation of the top of the tower is \(45^\circ \). The height of the flag staff is?
In ABC
AB=BC cot
AB= 5 m….(1)
In ABD
AB=BD cot
AB=(BC+CD)
AB=(5+CD) ….(2)
(5+CD) =5
CD=55
=5(0.732)=3.66 m
A tower subtends an angle \(\alpha \)at a point A in the place of its base and the angle of depression at the foot of the tower at a point B ft just above A is B. the height of the tower is?
In APQ
H= x tan …. (1)
In PRB
B=x tan ……(2)
B=
The angle of elevation of the top of a tower from certain point is \(30^\circ \). If the observer moves 20 m towards the tower, the angle of elevation of the top increases by \(15^\circ \) .the height of the tower is?
Tan =
H=x
Tan =