Question

3. 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% !
the ground. What should be the length of the slide in each case?​

Answer 1

Answer:

For the children below 5 years:-

Here , the perpendicular support is of 1.5m and inclined at 30°

so

tan 30° = 1/√3

tan = perpedicular/base

1/√3 = 1.5/b

b = 1.5*√3 [cross multiplication]

b = 2.6m

For elder children

same method

tan 60° = √3

√3 = 3/ b

b = 3/√3

b = 1.73 m

Hope it helps !!

Answer 2

Let, ABC is the slide inclined at 30° with length AC and PQR is the slide inclined at  60° with length PR.

To Find: AC and PR

In right ΔABC,

sin 30° = AB/AC

1/2 = 1.5/AC

AC = 3

Also,

In right ΔPQR,

sin 60° = PQ/PR

⇒ √3/2 = 3/PR

⇒ PR = 2√3

Hence, length of the slide for below 5 = 3 m and

Length of the slide for elders children = 2√3 m