Question

A rhombus of side 20cm has two angles of 60 each .Find the length of diagonals

Answer 1

The length of one diagonal = 2 *20cos(60)= 20 cm
The length of the other diagonal = 2 *20sin(60) = 20sqrt(3) cm

Answer 2

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

✒ ʟᴇᴛ ᴀʙᴄᴅ ʙᴇ ᴀ ʀʜᴏᴍʙᴜs ᴏғ sɪᴅᴇ 20 ᴄᴍ. ᴀɴᴅ ᴀɴɢʟᴇ ʙᴀᴅ = ᴀɴɢʟᴇ ʙᴄᴅ = 60°

ɴᴏᴛᴇ ᴛʜᴀᴛ ᴛʜᴇ ᴅɪᴀɢᴏɴᴀʟs ᴏғ ᴀ ʀʜᴏᴍʙᴜs ᴀʀᴇ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ʙɪsᴇᴄᴛᴏʀs ᴏғ ᴀɴɢʟᴇ ʙᴀᴅ ᴀɴᴅ ᴀɴɢʟᴇ ᴀʙᴄ ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ.

sᴏ, ∆ ᴀᴏʙ ɪs ᴀ ʀɪɢʜᴛ ᴛʀɪᴀɴɢʟᴇ sᴜᴄʜ ᴛʜᴀᴛ ᴀɴɢʟᴇ ʙᴀᴏ = 30°, ᴀɴɢʟᴇ ᴀᴏʙ = 90° ᴀɴᴅ ᴀʙ= 20 ᴄᴍ.

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴄᴏs ᴀɴɢʟᴇ ʙᴀᴏ = ᴏᴀ/ᴀʙ

=> ᴄᴏs 30° = ᴏᴀ/20

=> √3/2 = ᴏᴀ/20

=> ᴏᴀ = √3/2 × 20 = 10√3

ᴀʟsᴏ,

sɪɴ ᴀɴɢʟᴇ ʙᴀᴏ = ᴏʙ/ᴀʙ

=> sɪɴ 30° = ʙᴏ/20

=> 1/2 = ʙᴏ/20

=> ʙᴏ = 20/2 = 10

ᴛʜᴇʀᴇғᴏʀᴇ,

✴ ᴀᴄ= 2

✴ ᴀᴏ= 2 × 10√3 = 20√3 ᴄᴍ,

✴ ʙᴅ= 2

✴ ʙᴏ = 2 × 10 = 20 ᴄᴍ.

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