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Triangle ABC has AB=BC, AC = 16, and angle B = 90 degrees.  AC is extended to D such that BD=17.  Find the length of CD.

 

 Jan 9, 2021
 #1
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Triangle ABC is a 45-45-90  right triangle

 

BC   =16/sqrt (2)  =   8sqrt (2)  = sqrt ( 128)

 

Angle  BCD  = 180 - 45 =  135°

 

Using  the Law of Cosines

 

BD^2  =  CD^2  + BC^2  - 2( CD * BC)  cos (135°)

 

289  = CD^2  + 128  - 2 (CD * 8sqrt (2)) ( - sqrt (2) / 2)

 

289 - 128   =   CD ^2   +  16CD

 

161 =  CD^2 + 16CD

 

CD^2  + 16CD    -  161   =  0    factor

 

(CD   + 23) ( CD   -7)   =   0

 

The second factor  set  =  0   and solved gives us  that  CD =  7

 

 

cool cool cool

 Jan 9, 2021

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