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?
Solution:
(i) For the children below the age of 5 years,
Height of the slide = 1.5 m
Slide’s angle with the ground = 30°
(ii) For elder children,
Height of the slide = 3 m
Slide’s angle with the ground = 60°
Let us consider the following conventions for the slide installed for children below 5 years:
The height of the slide is AC.
Distance between the foot of the slide to the point where it touches the ground as AB.
We take the length of the slide as BC.
Let us consider the following conventions for the slide installed for elder children:
The height of the slide PR.
Distance between the foot of the slide to the point where it touches the ground as PQ.
We take the length of the slide as QR.
(i) Trigonometric ratio involving AC, BC and ∠B is sinθ
(ii) Trigonometric ratio involving PR, QR and ∠Q is sinθ
(i) In ΔABC,
sin 30° = AC / BC
1/2 = 1.5 / BC
BC = 1.5 × 2
BC = 3
(ii) In ΔPRQ,
sin Q = PR / QR
sin 60° = 3 / QR
√3/2 = 3 / QR
QR = (3 × 2) / √3
= (6 × √3) / (√3 × √3)
= 6√3 / 3
= 2√3
Length of the slide for children below 5 years = 3 m
Length of the slide for elder children = 2√3 m
☛ Check: Class 10 Maths NCERT Solutions Chapter 9
Video Solution:
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?
Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 3
Summary:
If 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 1.5m 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, then the length of the slide in each case will be 3m and 2√3m respectively.
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