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An aeroplane flying horizontally at a height of 3 Km, above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is

230.63 m/sec
230.93 m/sec
235.85 m/sec
235.85 m/sec

1094 Views

12.

If the angle of elevation of the sun decreases from 45° to 30°, then the length of the shadow of a pillar increases by 60m. The height of the pillar is

$60 left parenthesis square root of 3 plus 1 right parenthesis space metre$
$30 left parenthesis square root of 3 minus 1 right parenthesis space metre$
$30 left parenthesis square root of 3 plus 1 right parenthesis space metre$
$30 left parenthesis square root of 3 plus 1 right parenthesis space metre$

1180 Views

13.

The angle of elevation of the top of a tower, vertically erected in the middle of a paddy field, from two points on a horizontal line through the foot of the tower are given to be α and β (α>β). The height of the tower is h unit. A possible distance (in the same unit) between the points is

$fraction numerator straight h left parenthesis cot space straight beta space minus space cot space straight alpha right parenthesis over denominator cos space left parenthesis straight alpha space plus space straight beta right parenthesis end fraction$
$straight h space left parenthesis cot space straight alpha space minus space cot space straight beta right parenthesis$
$fraction numerator straight h left parenthesis tan space straight beta space minus space tan space straight alpha right parenthesis over denominator tan space straight alpha space tan space straight beta end fraction$
$fraction numerator straight h left parenthesis tan space straight beta space minus space tan space straight alpha right parenthesis over denominator tan space straight alpha space tan space straight beta end fraction$

1133 Views

14.

The angle of elevation of the top of an unfinished pillar at a point 150 metres from its base is 30°. The height (in metres) that the pillar must be raised so that its angle of elevation at the same point may be 45°, is (takeing √3 = 1.732)

63.4
86.6
126.8
128.6

901 Views

15.

From the top of a tower of height 180 m the angles of depression of two objects on either sides of the tower are 30° and 45°. Then the distance between the objects are

$180 space open parentheses 3 plus square root of 3 close parentheses straight m$
$180 space left parenthesis 3 minus square root of 3 right parenthesis straight m$
$180 space left parenthesis square root of 3 space minus 1 right parenthesis straight m$
$180 space left parenthesis square root of 3 space minus 1 right parenthesis straight m$

277 Views

16.
A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend an angle twice as before. The height of the tower is

80 m

100 m

160 m

160 m

80 m

From the figure, we have:

tan space straight theta space equals space straight h over 160 space space space and space tan space 2 straight theta space equals space straight h over 60 space space space space space space space... left parenthesis straight i right parenthesis

As we know,

tan space 2 straight theta space equals space fraction numerator 2 space tanθ over denominator 1 minus tan squared straight theta end fraction

∴ From point (i), we have

tan space 2 straight theta space equals space fraction numerator 2 tanθ over denominator 1 minus tan squared straight theta end fraction space space or space space space straight h over 60 space equals space fraction numerator 2 space cross times begin display style straight h over 160 end style over denominator 1 minus begin display style fraction numerator straight h squared over denominator left parenthesis 160 right parenthesis squared end fraction end style end fraction

rightwards double arrow space space straight h over 60 space equals space fraction numerator 2 straight h over denominator 160 end fraction cross times space fraction numerator left parenthesis 160 right parenthesis squared over denominator left parenthesis 160 plus straight h right parenthesis thin space left parenthesis 160 minus straight h right parenthesis end fraction

or, (160 + h) (160 - h) = 160 x 2 x 60
⟹ (160 + h) (160 - h) = 80 x (2 x 2 x 60)
⟹ (160 + h) (160 - h) = 80 x 240
We can see that h = 80 satisfies the equation hence height of the tower is 80 m.

694 Views

17.

The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is

187 Views

18.

The length of a shadow of a vertical tower is $fraction numerator 1 over denominator square root of 3 end fraction$ times its height. The angle of elevation of the Sun is

30°
45°
60°
60°

457 Views

19.

Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in metres) of the shorter post is

$fraction numerator straight x over denominator 2 square root of 2 end fraction$
$straight x over 4$
$straight x square root of 2$
$straight x square root of 2$

145 Views

20.

An aeroplane when flying at a height of 5000m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively. The vertical distance between the aeroplanes at that instant is

$5000 left parenthesis square root of 3 minus 1 right parenthesis space straight m$
$5000 space left parenthesis 3 minus square root of 3 right parenthesis space straight m$
$5000 open parentheses 1 minus fraction numerator 1 over denominator square root of 3 end fraction close parentheses straight m$
$5000 open parentheses 1 minus fraction numerator 1 over denominator square root of 3 end fraction close parentheses straight m$