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

Try another example


Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Do you want to convert length units?
See also our right triangle calculator.
Do you want to convert time units like minutes to seconds?
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:

Units of physical quantities:

Grade of the word problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: