ABD = 42 degrees , AD = AC = 12 units and AB = 14 units.Calculate DAC

Question

anonymous · Answer

yes , just a minute

anonymous · Answer

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rulnick · Answer

ACD is isosceles (not as shown, but based on info given).
Is BAC a right angle?

anonymous · Answer

no its not

anonymous · Answer

can you show me the calculations please ?

radar · Answer

Sometimes a drawing will mislead.  This one particulariy so.  The triangle on the left ABD, the angle ADB can be computed by using the law of sines.: 12/sin 42=14/sin BDA giving
Sin BDA=(14 sin 42)/12=.780652 The measure of the angle would be the inverse of this and is 51.3 degree not  a right angle.  Now if line segment BC is a straight line as it appears, then angle CDA is 180 degrees minus the 51.3 or angle CDA is 128.7 degrees
We were given that two of the legs were equal to 12, which means the other two angles would be equal to (180-128.6)/2=25.7 degrees each.  This is resulting in skewed triangle with a strange configuration.  Or am I just doing it wrong?