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+1
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avatar+925 

The isosceles trapezoid shown has side lengths as labeled. How long is segment AC?

Thanks!

AnonymousConfusedGuy  Mar 23, 2018
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2+0 Answers

 #1
avatar+85759 
+1

Draw  DE  perpendicular to  AB

Then  ADE  forms a right triangle  with  AE  =  (21 -9 ) / 2   = 12/2  =  6

 

Now....cos angle DAE  = (6/10)  =  3/5

And angle ABC  is supplemental to this...so its cos  =  -3/5

 

And we can use the Law of Cosines to find AC

 

AC  =  sqrt  [ AD^2 + DC^2  - 2(AD * DC)cos (ABC) ]

 

AC  = sqrt [ 10^2  + 9^2 - 2 (10 * 9) (-3/5) ]

 

AC  = sqrt [ 181  + 108 ]

 

AC = sqrt [289 ] =    17

 

 

cool cool cool

CPhill  Mar 23, 2018
edited by CPhill  Mar 23, 2018
 #2
avatar+925 
+1

Thank you!

AnonymousConfusedGuy  Mar 23, 2018

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