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The Map given here shows the state of Himachal Pradesh. On this map, $1 cm$ represents $29 km$ . Read this map carefully and using it, answer the following question.

About how many kilometres away is Mandi from Shimla $?$ If the distance between them on the map is $2 cm ?$

If the required answer is $X km$ , then write the value of $X$ in answer box.

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Important Questions on Position and Transformation

EASY

Mathematics>Geometry>Position and Transformation>Maps and Plans

As observed from the top of the light house, the angles of depression of two ships

P

and

Q

, anchored in the sea to the same side of the light house, are found to have measures

35 °

and

50 °

respectively. Then from the light house _____

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

Two vertical poles are

150 m

apart and the height of one is three times that of the other. If from the middle point of the line joining their feet, an observer finds the angles of elevation of their tops to be complementary, then the height of the shorter pole (in meters) is:

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

A tower stands vertically on the ground. From a point on the ground, which is

15 m

away from the foot of the tower, the angle of elevation from the top of the tower is found to be

30 °

. The height of the tower is:

EASY

Mathematics>Geometry>Position and Transformation>Maps and Plans

A boy observed

20 m

away from the base of a

20 m

high pole, the angle of elevation of the top is _____

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

P Q R

is a triangular park with

P Q = P R = 200 m

. A T.V. tower stands at the mid-point of

Q R

. If the angles of elevation of the top of the tower at

P, Q

and

R

are respectively,

45 °, 30 °

and

30 °

, then the height of the tower (in

m

) is:

EASY

Mathematics>Geometry>Position and Transformation>Maps and Plans

When a pole

6 m

high casts a shadow

2 \sqrt{3} m

long on the ground, then the angle of elevation of the sun is

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

A spherical gas balloon of radius

16

meter subtends an angle

60 °

at the eye of the observer

A

while the angle of elevation of its center from the eye of

A

75 °

. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

If a flagstaff of

6

metres height placed on the top of a tower throws a shadow of

2 \sqrt{3} m

along the ground, then the angle (in degrees) that the sun makes with the ground is

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

A B C

is a triangular park with

A B = A C = 100

metres. A vertical tower is situated at the mid-point of

B C

. If the angles of elevation of the top of the tower at,

A

and

B

are

{c o t}^{- 1} (3 \sqrt{2})

and

{c o s e c}^{- 1} (2 \sqrt{2})

respectively, then the height of the tower (in metres) is

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

The angle of elevation of a jet plane from a point

A

on the ground is

60 ° .

After a flight of

20

seconds at the speed of

432 km / hour

, the angle of elevation changes to

30 ° .

If the jet plane is flying at a constant height, then its height is:

HARD

Mathematics>Geometry>Position and Transformation>Maps and Plans

The angle of elevation of the top of a ladder leaning against a wall measured from a distance of

7.3

meters from the foot of the ladder is

45 °

. Suppose that the vertical height of the top of the ladder is

17.3

metres. Then, the best approximation of the angle of inclination of the ladder with the wall is:

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

Let a vertical tower

A B

have its end

A

on the level ground. Let

C

be the mid-point of

A B

and

P

be a point on the ground such that

A P = 2 A B

. If

∠ B P C = β

, then

\tan β

is equal to:

EASY

Mathematics>Geometry>Position and Transformation>Maps and Plans

If ratio of length of a vertical rod and length of its shadow is

\sqrt{3} : 1

, then the angle of elevation of sun will be

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

A bird is sitting on the top at a vertical pole of height

20 m

and elevation from a point

0

on the ground is

45^{°}

. The bird from the top of the pole flies off horizontally away from the pole. After one second, the elevation of the bird from

0

is reduced to

30^{°}

, then the speed of the bird is

EASY

Mathematics>Geometry>Position and Transformation>Maps and Plans

If the shadow of

10

m high tree is

10 \sqrt{3}

m, then the angle of elevation of sun is

EASY

Mathematics>Geometry>Position and Transformation>Maps and Plans

Let

A B

and

P Q

be two vertical poles,

160 m

apart from each other. Let

C

be the middle point of

B

and

Q

, which are feet of these two poles. Let

\frac{π}{8}

and

θ

be the angles of elevation from

C

P

and

A

, respectively. If the height of pole

P Q

is twice the height of pole

A B

, then

\tan^{2} θ

is equal to

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

If the angles of elevation of the top of a tower from two points at the distances of

3 m

and

12 m

from the base of the tower in the same straight line with it are complementary, then the height of the tower (in

m

) is

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point

A

, with uniform speed. At that point, angle of depression of the boat with the man's eye is

30 °

(Ignore man's height). After sailing for

20

seconds, towards the base of the tower (which is at the level of water), the boat has reached a point

B

, where the angle of depression is

45 ° .

Then the time taken (in seconds) by the boat from

B

to reach the base of the tower is :

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes

18 \min

for the angle of depression of the car to change from

30 °

45 °

, then the time taken (in

\min

) by the car to reach the foot of the tower is

MEDIUM

Mathematics>Geometry>Position and Transformation>Maps and Plans

An aeroplane flying at a constant speed, parallel to the horizontal ground,

\sqrt{3} km

above it is observed at an elevation of

60^{°}

from a point on the ground. If after five seconds, its elevation from the same point is

30^{°}

, then the speed (in

km / hr

) of the aeroplane is

Important Questions on Position and Transformation

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