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In triangle ABC, the angle bisector of BAC meets ¯BC at D. If BAC=45, ABC=45, and AD=24, then find the area of triangle ABC.

 Mar 12, 2024
 #1
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45  A

         24

 

   C           D              B 45

 

Angle CAD  =22.5   Angle CDA = 67.5   Angle ACD =  90

AC / sin (CDA)  = AD / sin (ACD)

AC/ sin (67.5) = 24 / 1

AC = 24sin (67.5)

 

BAC = 45    = ABC

So  BC  = AC

 

Area =  (1/2)(BC * AC)  =  (1/2)[ 24 sin (67.5)] ^2  ≈   245.8 

 

 

cool cool cool

 Mar 12, 2024

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