Question

The horizontal distance between two buildings is 140m .the angle of the top of the first building when seen from the top of the second building is 60°if the height of the first building is60m find the height of the second building

Answer 1

Hii

ʟᴇᴛ ᴀʙ ʙᴇ ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏғ sᴇᴄᴏɴᴅ ᴛᴏᴡᴇʀ ᴀɴᴅ ᴄᴅ ʙᴇ ᴛʜᴇ ʜᴇɪɢʜᴛ ᴏғ ғɪʀsᴛ ᴛᴏᴡᴇʀ.

ɢɪᴠᴇɴ, ʙᴅ = ᴀᴇ = 140 ᴍ

& ᴀʙ = ᴅᴇ = 60 ᴍ

ɪɴ Δᴀᴇᴄ,

ᴛᴀɴ 30°= ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ /ʙᴀsᴇ= ᴄᴇ/ᴀᴇ

ᴛᴀɴ 30 ° = ᴄᴇ/140

1/√3= ᴄᴇ /140

ᴄᴇ= 140 / √3

ᴄᴇ= 140 ×√3/ (√3×√3)

[ ʀᴀᴛɪᴏɴᴀʟɪsɪɴɢ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ]

ᴄᴇ= 140√3 /3

ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ғɪʀsᴛ ᴛᴏᴡᴇʀ ᴄᴅ= ᴄᴇ+ᴅᴇ

= 140√3/3 + 60

=( 140 × 1.73) /3 + 60

[ √3=1.73]

= 242.2/3 + 60

= 80.73 + 60

= 140.73 ᴍ

ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ғɪʀsᴛ ᴛᴏᴡᴇʀ (ᴄᴅ)=140.73ᴄᴍ

Thank You