a central angle intercepts an arc of 9in. if the radius of the circle is 2ft., deermine the measure of the central angle in Radians and Degrees. thanks i'm clueless!
2007-02-06 04:28:03 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
diameter = 4 feet or 48 "
circumference = π * d
circumference = 48π
48π/2π(radians) = 9/x
24=9/x
x=9/24
x=3/8 (radians)
x=.375
360/2π=y (degrees) /(3/8)
y=360*(3/8)/2π
y=360*3/(2*8π)
y=21.5º
2007-02-06 04:33:38 · answer #1 · answered by bequalming 5 · 0⤊ 0⤋
In radians
Angle =arc length/radius
=9/2
To convert degrees to radians, first convert the number of degrees, minutes, and seconds to decimal form. Divide the number of minutes by 60 and add to the number of degrees. So, for example, 12° 28' is 12 + 28/60 which equals 12.467°. Next multiply by and divide by 180 to get the angle in radians.
2007-02-06 12:37:48 · answer #2 · answered by jnjn 2 · 0⤊ 0⤋
The radius is 24 inches and the whole circunference mesures
2pi*r and corresponds to a central angle of 360 degrees or 2pi radians
So 150.8 inches =>360degrees => 2pi rad
9 " => 360/150.8 *9 degrees => 2pi *9/150.8 rad
The angle is 21.48degres =21deg29´ or 0.375 radians
2007-02-06 12:44:11 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋