Question

1.the perimeter of sector of a circle whose central angle is 90 and radius is 7cm is
2.a thin wire is in the shape of circle of radius 77cm.is bent into a square the side of square is
3.angle in major segment is
4.sum of angles in pentagon is
5. if A is an acute angle of ABC triangle right angled at B then value of sinA+cosA is

Answer 1

Perimeter = Ф  R,  where  Ф = central angle of sector of circle in radians
Perimeter for central angle of 90 deg
        =  π/2 * R = 22 / 7 * 1/2 * 7 cm =  11 cm
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length of wire = perimeter of circle = 2π *77 = 484 cm
perimeter of square = 4 * side = 484 cm
side = 121 cm
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  Angle made by a side of regular pentagon at the center  = 360 / 5 = 72 deg
   Sum of the two equal base angles at the side = 180 - 72 = 108 deg.
  Hence, Internal angle at one vertex = 108 deg.
   Sum of all 5 internal angles of pentagon = 540 deg.
             Formula =    π [ n - 2 ]
 ====================
 
  A = acute  B = 90 deg    C = acute angle
   Sin A + Cos A = Sin A + Cos (180 - 90 - C)
          =  Sin A + Sin C = 2 Sin (A+C)/2  Cos (A-C)/2
         =  2 SIn 45  Cos (A-C)/2  =  √2 Cos (A-C)/2

Or,  simply
   Sin A + Cos A  =  opposite side / hypotenuse  + adjacent side / hypotenuse
           = (AB + BC) / AC

  ====
   square that   =>  [ AB² + BC² + 2 AB BC ]  / AC²
             = 1 + 2 AB * BC / AC²
     so answer =  square root of that.