knowledge-route Maths10 Cha3
title: “Lata knowledge-route-Class10-Math1-2 Merged.Pdf(1)” type: “reveal” weight: 1
HEIGHTS & DISTANCES
HEIGHTS & DISTANCES
12.1 ANGLE OF ELEVATION :
In order to see an object which is at a higher level compared to the ground level we are to look up. The line joining the object and the eye of the observer is known as the line sight and the angle which this line of sight makes with the horizontal drawn through the eye of the observer is known as the angle of elevation. Therefore, the angle of elevation of an object helps in finding out its height (figure)
HEIGHTS & DISTANCES
12.2 ANGLE OF DEPRESSION :
When the object is at a lower level tan the observer’s eyes, he has to look downwards to have a view of the object. It that case, the angle which the line of sight makes with the horizontal thought the observer’s eye is known as the angle of depression (Figure).
HEIGHTS & DISTANCES
HEIGHTS & DISTANCES
ILLUSTRATIONS :
Ex. 1 A man is standing on the deck of a ship, which is
[CBSE - 2005]
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Sol. Let
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In right triangle
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Ex. 2 A vertical tower stands on a horizontal plane and is surmounted by vertical flag staff of height 5 meters. At a point on the plane, the angle of elevation of the bottom and the top of the flag staff are respectively
[CBSE-2006]
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Sol. Let
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In
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From (i) and (ii)
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Ex. 3 The angles of depressions of the top and bottom of
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Sol. Let
In
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In
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Form (i) and (ii)
Form (ii)
So,
Distance between two building
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Ex. 4 The angle of elevation of an aeroplane from a point on the ground is
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Sol. Let the point on the ground is
In
In
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From equation (i) and (ii)
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Hence, the speed of aeroplane is
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Ex. 5 If the angle of elevation of cloud from a point
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Sol. Let
In
In
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From (i) & (ii)
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Substituting the value of
Hence, the distance of the cloud from the point of observation is
Hence Proved.
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Ex. 6 A boy is standing on the ground and flying a kite with
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Sol. Let the length of second string
In
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In
DAILY PRACTICE PROBLEMS 12
OBJECTIVE DPP - 12.1
1. Upper part of a vertical tree which is broken over by the winds just touches the ground and makes an angle of
(A) 20 metres
(B)
(C) 10 metres
(D)
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Que. | 1 |
---|---|
Ans. | C |
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2. The angle of elevation of the top of a tower as observed from a point on the horizontal ground is ’
(A)
(B)
(C)
(D)
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Que. | 2 |
---|---|
Ans. | A |
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3. The angle of elevation of the top of a tower, as seen from two points A & B situated in he same line and at distances ’
(B)
(C)
(D) noen of these
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Que. | 3 |
---|---|
Ans. | C |
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4. The angle of elevation of the top of a tower at a distance of
(A)
(B)
(C) -50 metres
(D) 50 metres
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Que. | 4 |
---|---|
Ans. | D |
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5. The Shadow of a tower, when the angle of elevation of the sun is
(A)
(B)
(C)
(D) None of these.
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Que. | 5 |
---|---|
Ans. | C |
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SUBJECTIVE DPP - 12.2
1. From the top a light house, the angles of depression of two ships of the opposite sides of it are observed to be
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2. A ladder rests against a wall at angle
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3. From an aeroplanne vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stone on opposite side of aeroplane are observed to be
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4. A round balloon of radius ’
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5. A window in a building is at a height of
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Sol. 5.
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6. A man on a cliff observers a boat at an angle of depression of
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Sol. 6.
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7. The angles of elevation of the top of a tower two points ’
from the base and in the same straight line with it, are complementary. Prove that the height of the tower is
[CBSE - 2004]
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8. Two pillars of equal height are on either side of a road, which is
[CBSE - 2005]
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Sol. 8. Height
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9. At a point, the angle of elevation of a tower is such that its tangent is
[CBSE - 2006]
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Sol. 9.
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10. From a window ’
[CBSE - 2006]
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11. A pole
[CBSE - 2007]
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Sol. 11.
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12. The angle of elevation of a jet fighter from a point
[CBSE - 2008]
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Sol. 12.