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

 

 Mar 16, 2021
 #1
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Angle AOX  = 30°

 

sin AOX   = AX /  AO

 

sin 30°  AX /  20

 

20sin 30  =  AX

 

20 (1/2)  = AX  =  10

 

OX  = sqrt  ( AO^2  -  AX^2)  =   sqrt ( 20^2  - 10^2)  =  sqrt (300)   =  10sqrt (3)

 

XY  =  OY -  OX  =   20  -10sqrt(3)   =  10  ( 2  - sqrt (3) )  ≈  2.679

 

cool cool cool 

 Mar 16, 2021

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