Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 13

EASY

NDA & NA EE

IMPORTANT

Earn 100

A spherical balloon of radius $r$ subtends an angle $α$ at the eye of an observer, while the angle of elevation of its centre is $β .$ What is the height of the centre of the balloon (neglecting the height of the observer)?

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Important Questions on Heights and Distances

MEDIUM

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 14

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:

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 15

A chimney

20 m

high standing on the top of a building subtends an angle whose tangent is

\frac{1}{6}

at a distance

70 m

from the foot of the building. The height of the building is

HARD

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 16

A man walks

10 m

towards a lamp post and notices that the angle of elevation of the top of the post increases for

30 °

to

45 ° .

The height of the lamp post is

MEDIUM

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 17

A tree is broken by wind, its upper part touches the ground at a point

10 m

from the foot of the tree and makes an angle of

45 °

with the ground. The entire length of the tree is

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 18

At a point

15 m

away from the base of a

15 m

high house, the angle of elevation of the top is

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 19

If the elevation of the Sun is

30 °,

then the length of the shadow cast by a tower of

150 ft

height, is

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 20

If a flagstaff subtends equal angles at the points

A, B, C

and

D

on the horizontal ground through the foot of flagstaff, then the points

A, B, C

and

D

necessarily form a

EASY

NDA & NA EE

IMPORTANT

Mathematics Crash Course NDA & NA EE>Chapter 8 - Heights and Distances>Exercise 1>Q 21

A ladder rests against a wall, so that its top touches the roof of the house. If the ladder makes an angle of

60 °

with the horizontal and height of the house be

6 \sqrt{3} m,

then the length of the ladder is