# 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

1
by safura

2015-01-14T00:11:23+05:30

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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 ]
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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

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