In a circle of radius 48 cm, an arc 76 cm long subtends an angle of how many radians, and how many degrees?

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In a circle of radius 48 cm, an arc 76 cm long subtends an angle of how many radians, and how many degrees?

The answer must be a simplified fraction

2007-10-26 06:59:47 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

C = 2 π r
C = 96 π cm
96π cm<----->2π radians
76 cm<--->(76 / (96π)) x 2π radians
= 1.58 radians

2π radians <---> 360°
1.58 radians<-->(1.58/2π) x 360°
= 90.6°

2007-10-30 05:42:59 · answer #1 · answered by Como 7 · 1⤊ 0⤋

The circumferance is 2pi*r=2*3.141593*48=301.6 cm
the arc is 76 cm or 76/301.6=25.2% of the circumference.

2pi radians=360 degrees.

so the arc subtends 25.2% of 2pi or 1.58 radians
also the arc subtends 25.2% 0f 360 or 90.7 degrees

2007-10-26 07:30:55 · answer #2 · answered by frozen 5 · 0⤊ 1⤋