1.5 m

30º

3 m

Q. A contractor plans to install two slides for the children to play in a park.

For the children below the age of 5 years, she prefers to have a slide whose

top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground,

whereas for elder children, she wants to have a steep slide at a height of 3m,

and inclined at an angle of 60° to the ground. What should be the length of the

slide in each case?

60º

?

?

A

B

C

P

Q

R

Sol.

Let the length of slide for the children

below 5 years (AC) be ‘x’ m

Length of slide for the elder

children (PR) be ‘y’m

Height of 1^st slide (AB) = 1.5 m

Height of 2^nd slide (PQ) = 3 m

For small children :

In right ΔABC,

sin 30º

=

AB

AC

∴

1

2

=

1.5

x

∴

x

=

1.5

× 2

∴

x

=

3

P

Q

R

3 m

y

60º

Q. A contractor plans to install two slides for the children

to play in a park. For the children below the

age of 5 years, she prefers to have a slide whose

top is at a height of 1.5 m, and is inclined at

an angle of 30° to the ground, whereas for

elder children, she wants to have a steep

slide at a height of 3m, and inclined at an

angle of 60° to the ground.

What should be the length of the slide in each case?

Ratio of opposite side and Hypotenuse reminds us of _________

‘sin’

Observe ∠C

For ‘∠C’

Opposite side →

Hypotenuse →

AB

AC

?

A

B

C

1.5 m

x

30º

Opposite

side

hypotenuse

?

sin 30^o =

?

6

3

2

Q. A contractor plans to install two slides for the children

to play in a park. For the children below the

age of 5 years, she prefers to have a slide whose

top is at a height of 1.5 m, and is inclined at

an angle of 30° to the ground, whereas for

elder children, she wants to have a steep

slide at a height of 3m, and inclined at an

angle of 60° to the ground.

What should be the length of the slide in each case?

For elder children :

In right ΔPQR,

sin 60º

=

PQ

PR

∴

2

=

3

y

∴

=

3

× 2

∴

y

=

6

∴

y

=

6

×

∴

y

=

∴

y

=

2

Length of slide for children below 5 years is 3 m

and length of slide for elder children is 3.46 m

Opposite

side

hypotenuse

Observe ∠R

∴

Let us rationalise the denominator

y

=

2 × 1.73

=

3.46

∴

Sol.

P

Q

R

3 m

y

60º

A

B

C

3m

30º

For ‘∠R’

Opposite side →

Hypotenuse →

PQ

PR

sin 60^o =

?

Ratio of opposite side and Hypotenuse reminds us of _________

‘sin’