Question

Construct a triangle ABC in which BC = 7 cm, B = 75° and AB + AC = 13 cm. Also,
Write the steps of construction.​

Answer 1

ɢɪᴠᴇɴ,

ᴛᴏ ᴄᴏɴsᴛʀᴜᴄᴛ ᴀ δᴀʙᴄ ᴡʜᴇʀᴇ 

ʙᴄ=7ᴄᴍ,∠ʙ=75∘ & ᴀʙ+ᴀᴄ=13ᴄᴍ.

ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ sᴛᴇᴘs :-

(ɪ) ᴅʀᴀᴡ ᴀ ʟɪɴᴇ sᴇɢᴍᴇɴᴛ ʙᴄ = 7 ᴄᴍ ᴀs ᴀ ʙᴀsᴇ.

(ɪɪ) ɴᴏᴡ ᴍᴀʀᴋ ∠ʙ=75∘ ᴀɴᴅ ᴇxᴛᴇɴᴅ ɪᴛ ᴛɪʟʟ x.

(ɪɪɪ) ɴᴏᴡ, ʙʏ ᴛᴀᴋɪɴɢ ʀᴀᴅɪᴜs 13 ᴄᴍ ᴅʀᴀᴡ ᴀɴ ᴀʀᴄ ғʀᴏᴍ 'ʙ' ᴏɴ ᴛʜᴇ ʟɪɴᴇ ᴏғ ᴀɴɢʟᴇ ᴊᴜsᴛ ᴘʀᴏᴊᴇᴄᴛᴇᴅ.

(ɪᴠ) ɴᴏᴡ ᴍᴀʀᴋ ɪᴛ ᴀs 'ᴅ', & ᴊᴏɪɴ ᴄ ᴛᴏ ᴅ.

(ᴠ) ᴅʀᴀᴡ ⊥ʟᴀʀ ʙɪsᴇᴄᴛᴏʀs ғᴏʀ ᴅᴄ ᴀɴᴅ ᴍᴀʀᴋ ᴛʜᴇᴍ ᴀs ᴘ & ǫ.

(ᴠɪ) ɴᴏᴡ ᴇxᴛᴇɴᴅ ᴀ ʟɪɴᴇ ғʀᴏᴍ 'ʙ' ᴛᴏ ᴛʜᴇ ⊥ʟᴀʀʙɪsᴇᴄᴛᴏʀ ᴛʜᴀᴛ ᴄᴜᴛs ᴏɴ ᴄ & ᴅ ʟɪɴᴇ.

(ᴠɪɪ) ɴᴏᴡ ᴍᴀʀᴋ ᴛʜᴀᴛ ᴘᴏɪɴᴛ ᴀs 'ᴀ'.

(ᴠɪɪɪ) ᴛʜᴜs, ʀᴇǫᴜɪʀᴇᴅ δᴀʙᴄ ʜᴀs ʙᴇᴇɴ ғᴏʀᴍᴇᴅ.

(ɪx) ɴᴏᴡ, ᴛʀʏ ᴛᴀᴋɪɴɢ ᴇxᴀᴄᴛʟʏ 1/2 ᴏғ ᴛʜᴇ ᴀɴɢʟᴇ ᴀɴᴅ ᴍᴀʀᴋ ᴀɴ ᴀʀᴄ ᴏɴ ʙ.

ᴄᴏɴᴄʟᴜsɪᴏɴ :-

∴ ᴛʜᴇ ʀᴇǫᴜɪʀᴇᴅ δᴀʙᴄ ᴡɪʟʟ ʙᴄ = 7 ᴄᴍ,

∠ʙ=45∘ & ᴀʙ + ᴀᴄ = 13 ᴄᴍ ɪs ᴄᴏɴsᴛʀᴜᴄᴛᴇᴅ.

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