Triangle 75

Triangle ABC has angle C bisected and intersects AB at D. Angle A measures 20 degrees and angle B measures 40 degrees. The question is determine AB-AC if length AD=1.

Correct answer:

x =  0.3949

Step-by-step explanation:

AD=1 A=20  B=40   C=180AB=1802040=120  ACD=C/2=120/2=60  DCB=C/2=120/2=60   ADC=180AACD=1802060=100  CDB=180BDCB=1804060=80   sinACDsinADC=AC:AD  AC=AD sinACDsinADC=AD sin60° sin100° =1 sin60° sin100° =1 0.8660250.984808=1.13716  DC=AD sinACDsinA=AD sin60° sin20° =1 sin60° sin20° =1 0.8660250.34202=0.39493  DB=DC sinBsinDCB=DC sin40° sin60° =0.3949 sin40° sin60° =0.3949 0.6427880.866025=0.53209  AB=AD+DB=1+0.53211.5321  x=ABAC=1.53211.1372=0.3949

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