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In the diagram, AOB is a sector of a circle with angle AOB = 60.  OY is drawn perpendicular to AB and intersects AB at X.  What is the length of AB?

 

 Jul 4, 2022
 #1
avatar+2293 
+1

Using the Law of Cosines on \(\triangle AOB\) gives us \(AB = \sqrt{20^2 + 20^2 - 2\times 20 \times 20 \cos 60} = \color{brown}\boxed{20}\)

 Jul 4, 2022
 #2
avatar+124526 
+1

Also.....notice that if angle AOB = 60

 

Then angle  AOX = 30  = angle BOX

 

And angle  OAB  = Angle BOA  =  60

 

So triangle   AOB is equilateral with AB  = 20

 

 

cool cool cool

 Jul 4, 2022

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