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Solve for x? Show the equation you used and your work.

Answer 1

Savannah Aguilar

#x=27#.

Since the Ray #AD# bisects the #/_BAC#, we know from Geometry,

that, #(BD)/(DC)=(AB)/(AC) rArr 24/18=36/x rArr x={(18)(36)}/24=27#

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Answer 2

Violet Aldrich

See below.

Applying the "sinus law"

#Delta ABD->sin(angle(BAC)/2)/bar(BD)=sin(angleBDA)/bar(BA)# #Delta ADC->sin(angle(BAC)/2)/bar(DC)=sin(angleADC)/x#

but #angleBDA+angleADC=pi# so #sin(angleBDA)=sin(angleADC)#

When we split the two relationships term by term, we arrive at

#bar(DC)/bar(BD)=x/bar(BA)# so

#x = (bar(BA)bar(DC))/bar(BD)=(36 cdot 18)/24=27#

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