Question

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, where as for the elder children she wants to have a steep side at a height of 3 m, and inclined at an angle of 60 ° to the ground. What should be the length of the slide in each case?

Answer 1

Answer:

Step-by-step explanation:

for children below the age of 5:

we know that sin=opposite /hypotenuse;

sin 30=1/2=1.5/hypotenuse

cross multiplying=

hypotenuse= 3m

slide for the younger children=3m

for elder children:

sin =opposite/hypotenuse

sin 60 = root3/2 =3/hypotenuse

cross multiplying=

hypotenuse=2root3m

slide for the older children=2root3

Answer 2

$\huge\mathfrak{Bonjour!!}$

$\huge\fcolorbox{black}{aqua}{Solution:-}$

✒ ʟᴇᴛ 'ᴀᴄ' ʙᴇ ᴀ sᴛᴇᴇᴘ sʟɪᴅᴇ ғᴏʀ ᴇʟᴅᴇʀ ᴄʜɪʟᴅʀᴇɴ ᴀɴᴅ 'ᴅᴇ' ʙᴇ ᴀ sʟɪᴅᴇ ғᴏʀ ʏᴏᴜɴɢᴇʀ ᴄʜɪʟᴅʀᴇɴ. ᴛʜᴇɴ ᴀʙ = 3ᴍ ᴀɴᴅ ᴅʙ= 1.5 ᴍ.

ɴᴏᴡ, ɪɴ ʀɪɢʜᴛ ᴀɴɢʟᴇ ∆ᴅʙᴇ, ᴡᴇ ʜᴀᴠᴇ

sɪɴ 30° = ʙᴅ/ᴅᴇ = 1.5/ᴅᴇ

=> 1/2 = 1.5/ᴅᴇ

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴅᴇ = 2 × 1.5 = 3 ᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ,

★ʟᴇɴɢᴛʜ ɪғ sʟɪᴅᴇ ғᴏʀ ʏᴏᴜɴɢᴇʀ ᴄʜɪʟᴅʀᴇɴ = 3 ᴍ.

ᴀɢᴀɪɴ, ɪɴ ʀɪɢʜᴛ ᴀɴɢʟᴇ ∆ᴀʙᴄ, ᴡᴇ ʜᴀᴠᴇ

sɪɴ 60° = ᴀʙ/ᴀᴄ

=> √3/2 = 3/ᴀᴄ

=> ᴀᴄ = 6/√3 × √3/√3 = 6√3/3

= 2√3 ᴍ.

sᴏ, ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ sʟɪᴅᴇ ғᴏʀ ᴇʟᴅᴇʀ ᴄʜɪʟᴅʀᴇɴ ɪs 2√3 ᴍ.

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