Question

The perimeter of a certain sector of a circle is equal to the length of the arc of the semi-circle having the same radius,express the angle of the sector in degrees, minutes and seconds.

Answer 1

Perimeter of sector= 2r +x (let x be the length of the arc)
length of the arc of the semi circle = pi*r
pi*r = 2r + x
x =pi*r - 2r
x= r(pi -2)=r(22/7-2)
x=r(8/7)
x=8/7r
angle of sector = 8/7r / r
=8/7 rad
=8/7 x 180/pi = 8/7 x 180/22 x 7 degrees
=720/11 degrees = 65.4545
=65 deg + 0.4545*60 minutes
=65 deg + 27.27 minutes
=65 deg + 27 minutes + 0.27*60 seconds
=65 deg+27 min+16 sec
=65 deg 27 min 16 sec.