What is the size in degrees, of the angle subtended by an arc of 1 2/3ft in a circle whose radius is 45 in..?

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What is the size in degrees, of the angle subtended by an arc of 1 2/3ft in a circle whose radius is 45 in..?

Plane Trigonometry

2007-07-11 15:38:29 · 3 answers · asked by Peter 1 in Science & Mathematics ➔ Mathematics

3 answers

45 in... the circumference would be 282.74 inches/23.56ft

23.56/1.666=14.136

360*1/14.136=25.47 degrees

i have no idea if that is even close to being right

2007-07-11 15:43:27 · answer #1 · answered by Jay 4 · 0⤊ 0⤋

C = 2 π r where r = 45 "
C = 90 π "
Arc length = 20 "
90 π<----> 360°
20 <-----> 360° x 20 / (90 π) = 80° / π = 25.5 °

2007-07-11 21:31:14 · answer #2 · answered by Como 7 · 0⤊ 0⤋

Two ways:

l = r*theta .... theta = l / r = 20/45 = 0.444 rad

For degrees: 57.2958 deg/1 rad * (0.444 rad) = 25.46 deg

-or-

theta / 360 = 20 / 2*pi*r
theta = (20*360)/ 2*pi*r
= 7200 / 282.74 = 25.46 deg

2007-07-11 16:00:06 · answer #3 · answered by Pro bono publico 4 · 0⤊ 0⤋