Solve it ......
and plz ans my previous questions...
i m giving you 10 points....
Answers
Hey there !
Interesting question !
Since Angle B = 90°, Δ ABC is a scalene triangle as it has different angle measures.
So let us apply trigonometry to find the respective sides.
Equation = AB + BC + AC = 11 cm
Now let us divide the whole equation by AC
=> AB / AC + BC / AC + AC / AC = 11 / AC
=> SinФ + Cos Ф + 1 = 11 / AC
=> Sin 60 + Cos 60 + 1 = 11 / AC
=> √ 3 / 2 + 1 / 2 + 1 = 11 / AC
Taking LCM as 2 and then adding the terms we get,
=> √ 3 + 2 + 2 / 2 = 11 / AC
=> 4 + √3 / 2 = 11 / AC
=> AC = 11 / ( 4 + √3 ) / 2
=> AC = 11 * 2 / 4 + √ 3 = 22 / 4 + √ 3
So AC = 22 / 4 + √ 3
=> AB / AC = √ 3 / 2
=> AB = √ 3 ( 22 + 4 √ 3 ) / 2
=> AB = 22 √3 + 12 / 12
=> AB = 2 ( 11 √3 + 6 ) / 2 ( 6 )
2 gets cancelled. We get,
=> AB = 11 √ 3 + 6 / 6
BC / AC = 1 / 2 ( ∵ Cos 60 = 1 / 2 )
=> BC = AC / 2
=> BC = 22 + 4√3 / 2
=> BC = 2 ( 11 + 2√3 ) / 2 ( 1 )
2 gets cancelled. We get,
=> BC = 11 + 2√3 units
Hence the values of the sides are :
AB = ( 11√3 + 6) / 6
BC = 11 + 2√3
AC = 22 / ( 4 + √3 )
Hope my answer is correct. If any mistakes, please let me know in the comments.
Cheers !
Answer:
AB = ( 11√3 + 6) / 6
BC = 11 + 2√3
AC = 22 / ( 4 + √3 )