Math mini-contest trigonometry problem for Day 7 on D.Buzz for May 2021 😎

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(Edited)

Math mini-contest problem for Day 7 on D.Buzz for May 2021 😎

Triangle FAN is circumscribed in a circle G. Fang already solved for the following in the circle:

  • NG = 4 meters
  • FN = 5 meters
  • AN = 6 meters

What should Fang's answer regarding the measure of arc FA be?

math mathematics dbuzz minicontest contest trigonometry geometry circle triangle
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I assume G is the center of the circle?
there are two isolecense triangles: GFN with sides 4, 4, 5 and GNA with sides 4, 4, 6. The angles at G are then 77.37 deg for GFN and 97.18 deg for GNA. The arc len FA is 2r*sin(a/2), with r=4, a=77.37+97.18 deg
=> FA = 7.75 meters
not sure if I got this...?!

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lol,missed the last step: arc length = 2r pi * a/360 = 12.18m

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