Circle's 81078

The chord of a circle is 233 long, and the length of the circular arc above the chord is 235. What is the circle's radius, and what is the central angle of the circular arc?

Correct answer:

r =  519.3083
Φ =  25.9278 °

Step-by-step explanation:

t=233 o=235  o = α ⋅  r sin α/2 = t/2 : r  r ⋅  sin α/2 = t/2 o/α ⋅  sin α/2 = t/2  2⋅ o ⋅  sin α/2 = α⋅ t  2⋅ 235 ⋅  sin α/2 = α⋅ 233 α=0.452525≐0.4525 rad  r=o/α=235/0.4525=519.3083
Φ=α→  °=α⋅ π180​   °=0.4525⋅ π180​   °=25.92777  °   Verifying Solution:  t2​=2⋅ r⋅ sin(α/2)=2⋅ 519.3083⋅ sin(0.4525/2)≐233 o2​=α⋅ r=0.4525⋅ 519.3083=235

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algebraplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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