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SAT, 16.12.2021 18:40 trent1002brown

Determine the value of $a$. [asy] pair w=(0,4); pair x=(0,0); pair y=(4,0); pair z=y+7/sqrt(2)*(1,1); dot(w); dot(x); dot(y); dot(z); draw(w--x--y--z--w); draw(0. 15*w--0. 15*w+0. 15*y--0. 15*y); label("$w$",w, nnw); label("$x$",x, sw); label("$y$",y, se); label("$z$",z, e); label("4",(w+x)/2,w); label("4",(x+y)/2,s); label("9",(w+z)/2,nnw); label("$a$",(y+z)/2,se); label("$135^\circ$",y, nnw); [/asy].

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Determine the value of $a$. [asy] pair w=(0,4); pair x=(0,0); pair y=(4,0); pair z=y+7/sqrt(2)*(1,1)...
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