Question 1193627
a/sin A=c/sin C and angle C is 105deg. Side c is AB.
14/sin45=x/sin 105
x=14*sin 105/sin45
=19.12
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Altitudes are perpendicular so triangle ADC is a right triangle and angle DCA is 45 degrees and angle DCB is 60 degrees.
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Get AC or side b as well: 14/sin 45=b/sin 30
sin 30 is 0.5
b=14 sin30/sin45=7/sqrt(2)/2 or 7 sqrt(2)=9.90, which is the hypotenuse.
The legs are each hyp/sqrt(2) or 7 The altitude is 7
That is also AD
So DB is 12.12
the right triangles are 7/7/9.9 and 12.12/7/14

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AD=x and DB is 19.12-x
ACD is a right triangle, so x^2+alt^2=7^2=49
(19-x)^2+49=196
(19-x)^2=147
19-x=12.12 AB approx
the exact value is sqrt(147)AB exact