Three horses trthered with 7m long rope at three corners
Of a triangular field having the sides 21m, 21√2m and 21m.
Find the area of the field on which each horse can graze.
Answers
Answer:
ꜱᴄɪᴇɴᴄᴇ, ᴀɴʏ ꜱʏꜱᴛᴇᴍ ᴏꜰ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴛʜᴀᴛ ɪꜱ ᴄᴏɴᴄᴇʀɴᴇᴅ ᴡɪᴛʜ ᴛʜᴇ ᴘʜʏꜱɪᴄᴀʟ ᴡᴏʀʟᴅ ᴀɴᴅ ɪᴛꜱ ᴘʜᴇɴᴏᴍᴇɴᴀ ᴀɴᴅ ᴛʜᴀᴛ ᴇɴᴛᴀɪʟꜱ ᴜɴʙɪᴀꜱᴇᴅ ᴏʙꜱᴇʀᴠᴀᴛɪᴏɴꜱ ᴀɴᴅ ꜱʏꜱᴛᴇᴍᴀᴛɪᴄ ᴇxᴘᴇʀɪᴍᴇɴᴛᴀᴛɪᴏɴ. ɪɴ ɢᴇɴᴇʀᴀʟ, ᴀ ꜱᴄɪᴇɴᴄᴇ ɪɴᴠᴏʟᴠᴇꜱ ᴀ ᴘᴜʀꜱᴜɪᴛ ᴏꜰ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴄᴏᴠᴇʀɪɴɢ ɢᴇɴᴇʀᴀʟ ᴛʀᴜᴛʜꜱ ᴏʀ ᴛʜᴇ ᴏᴘᴇʀᴀᴛɪᴏɴꜱ ᴏꜰ ꜰᴜɴᴅᴀᴍᴇɴᴛᴀʟ ʟᴀᴡꜱ. ꜱᴄɪᴇɴᴄᴇ.
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Step-by-step explanation:
Given,
Three horses trthered with 7m long rope at three corners of a triangular field having the sides AB= 21m, BC= 21m and AC=21√2m respectively.
To find:- The area of the field on which each horse can graze.
solution:-
In ∆ABC we have,
=> (AB)² +( BC)² = (AC)² [ Pythagoras theorem]
=> (21)² +( 21)² = (21√2)²
=> 441 + 441 = 441 × 2
=> 882. = 882.
So, From the above it is clear that ∆ABC is a Right isosceles triangle.
By angle sum property:
Angles ( CAB + ACB + ABC ) = 180°
x° + x° + 90° = 180°
2x° +90°= 180°
x° = 45°
Now,
The area of the field on which the horse at A and B can graze = π r² x°
360°
= 2/7 × 7× 7 × 45°
360°.
= 22×7× 45°
360°
= 19.25 m²
The area of the field on which horse at B can graze = π r² 90°
360°
= 2/7 × 7× 7 × 90°
360°.
= 22×7× 90°
360°
= 38.5 m².
Thanks....