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10th ICSE

IMPORTANT

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An aeroplane when flying at a height of $4000 m$ from the ground, passes vertically above another aeroplane at an instant, when the angles of the elevation of the two planes from the same point on the ground are $60 °$ and $45 °$ , respectively.The vertical distance between the aeroplanes at that instant is $k m$ . Find $k$ .

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Important Questions on Heights and Distances

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>CHAPTER EXERCISE>Q 39

The radius of a circle is given as

15 cm

and chord

A B

subtends an angle of

131 °

at the Centre

C

of the circle, using trigonometry. Then the length of

A B =

_____

m

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>CHAPTER EXERCISE>Q 39

The radius of a circle is given as

15 cm

and chord

A B

subtends an angle of

131 °

at the Centre

C

of the circle, using trigonometry. iF the distance of

A B

k cm

from centre

C

, then find

k

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>CHAPTER EXERCISE>Q 40

The angle of elevation of a stationary cloud from a point

25 m

above a lake is

30 °

and the angle of depression of its reflection in the lake is

60 °

. What is the height

(m)

of the cloud above that lake-level?

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>CHAPTER EXERCISE>Q 41

The angle of elevation of the top of a hill at the foot of a tower is

60 °

and the angle of elevation of the top of the tower from the foot of hill is

30 °

. If the tower is

50 m

high, then find the height of the hill in metres.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>CHAPTER EXERCISE>Q 42

The angle of elevation of the top

B

of a tower

A B

from a point

X

on the ground is

60 °

. At a point

Y

40 m

vertically above

X

, the angle of elevation of the top is

45 °

. Find the height of the tower

A B

and the distance

X B

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>ARCHIVES (Last 8 Years)>Q 1

The angle of elevation from a point $P$ of the top of tower $Q R$ , $50 m$ high is $60 °$ and that of the tower $P T$ from a point $Q$ is $30 °$ . Find the height of the tower (Correct upto two decimal places) $P T$ , connect to the nearest metre. $(Take \sqrt{3} = 1.73)$

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>ARCHIVES (Last 8 Years)>Q 2

The angle of depression of two ships

A

and

B

as observed from the top of a light-house

60 m

high are

60 °

and

45 °

, respectively. If the two ships are on the opposite sides of the light-house, then find the distance between the two ships. Give your answer correct to the nearest whole number.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 19 - Heights and Distances>ARCHIVES (Last 8 Years)>Q 3

An aeroplane at an altitude of

1500 m

finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are

45 °

and

30 °

, respectively. Find the distance between the two ships in metres.

Important Questions on Heights and Distances

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