Text Book Maths Problem - 7

Question

Change 1.234 radians to degrees, minutes and seconds.

 
Change 44degres 49' 53" to radians, expressed as a multiple of pi.

 
Calculate, correct to 2 decimal place accuracy, the perimeter of a sector which has an included angle of 75o and a radius of 6.2 m.

Answer 1

1.234 radians = 1.234(180)/pi degrees

= about 70.70298412 degrees

= about 70 degrees 42.179 minutes

= about 70 degrees 42 minutes and about 10.74 seconds

= about 70 degrees, 42' 11"

44 degrees 49' 53"

=44+ 49/60 +53/3600 degrees

= about 44.81666...+.0147222...degrees

= 44.8313888...degrees

=about .249063271pi radians

= about pi/4 radians

45 degrees = pi/4 radians

44 degrees, 49 minutes, 53 seconds = about 45 degrees

perimeter of a sector = arc length plus twice the radius

arc length = the radius time the angle in radians

= radius x radians

= 6.2 meters x 75pi/180

= 6.2(75pi)/180

= about 8.1158 meters

perimeter = 20.5158

= about 20.52 meters