Angle ASB

On a circle with a radius of 10 cm and with a center S, the points A, B, and C are given so that the central angle ASB is 60 degrees and the central angle ASC is 90 degrees. Find the length of the circular arc and the amount of AB and AC offsets.

Correct answer:

o1 =  10.472 cm
o2 =  15.708 cm
d1 =  10 cm
d2 =  14.1421 cm

Step-by-step explanation:

r=10 cm α=60  β=90   o=2π r=2 3.1416 1062.8319 cm  o1=360α o=36060 62.8319=10.472 cm
o2=360β o=36090 62.8319=15.708 cm
 sin α/2 = d1/2 : r  d1=2 r sin(α/2)=2 10 sin(60/2)=10 cm
 sin β/2 = d2/2 : r  d2=2 r sin(β/2)=2 10 sin(90/2)=10 2=14.1421 cm

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