Trigonometry 3d pyramid question

[needingtoknow]

Homework Statement

http://imgur.com/x8D2wqO

I need to solve for theta and I keep getting the angle 65, using cosine law and pythagorean theorem but the answer key says that the angle is 93. The diagram is not to scale. Is my answer wrong or is the answer key incorrect?

 

[haruspex]

It isn't quite clear what length is 15cm. Is it AC or AD? To get 93 degrees, it would probably have to be AC. Either way, there does not seem to be enough information. Please post your working.

 

[needingtoknow]

15 cm is AD

 

[needingtoknow]

c^2 = a^2 + b^2 - 2abcosC
c = 23.7471

h^2 = a^2 + b^2
h = 23.4307

h^2 = a^2 + b^2
h = 20.5183

(23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
theta = 65

 

[haruspex]

c^2 = a^2 + b^2 - 2abcosC
c = 23.7471

h^2 = a^2 + b^2
h = 23.4307

h^2 = a^2 + b^2
h = 20.5183

(23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
theta = 65

I can't be expected to follow that if you keep changing what the letters refer to and don't specify each time.

 

[whoareyou]

Using AD = 15cm, BD = 18cm, CD = 14cm and angle BDC = 95 degrees, I too get 65 degrees as angle BAC.

 

[needingtoknow]

c^2 = a^2 + b^2 - 2abcosC
c = 23.7471 Finding length of BC

h^2 = a^2 + b^2
h = 23.4307 Finding length of AB

h^2 = a^2 + b^2
h = 20.5183 Finding length of AC

(23.7471)^2 = (23.4307)^2 + (20.5183)^2 - 2(23.4307)(20.5183)costheta
theta = 65 Finding angle theta of triangle ABC

 

[haruspex]

After making some guesses about the other assignments in those equations, I'm led to suppose you are taking angles ADB, ADC to be right angles. I don't see that stated anywhere.
As I said, to get an angle of over 90 degrees as the answer, you will need the 15cm to refer to AC, not AD. OTOH, I then get 91.9 degrees, so it still doesn't seem quite right.

 

[needingtoknow]

All right so it must be a textbook answer key problem. Thank you very much for your help