Calculate unknowns in a set of triangles

I got a problem of which I can’t get mathematica to calculate.

The known inputs are a=17 degree, b=12 degree and side d is 300.

The whole thing is actually 4 right-angled triangles (left side as A, right side as B, the red at bottom as C and the black with the d side as D)

I’ve tried to type all the equations for the angles and sides I need to get the h value but I can’t get a reasonable output.

Remove["Global`*"]
va = 17;
vb = 12;
d = 300;    
Reduce[{(Tan[va]*(Tan[vc]*d)) == (Sin[va]*(Tan[vd]*d)) == (Tan[vb]*(Cos[vc]/d)) == (Sin[vb]*(Cos[vd]/d)), Tan[vc] == (Tan[vc]*d)/d, Cos[vc] == d/(Cos[vc]/d), Tan[vd] == (Tan[vd]*d)/d, Cos[vd] == d/(Cos[vd]/d)}, h] // N

The ouput I get is

Tan[vc] == -0.275163 Tan[vd] && Sec[vd] == 1.79174 Tan[vd] &&
Sec[vc] == 1.51196 Tan[vd] && Cos[vd] == 161256. Tan[vd] &&
Cos[vc] == 136077. Tan[vd]

What is it that I’m missing?
I can’t see how else I should make the equation more elaborate to get allt the sides and angles that is needed to the the value of h.

va = 17 Degree; vb = 12 Degree; d = 300;
Reduce[{(h == Tan[va]*(Tan[vc]*d)) == (Sin[va]*(Tan[vd]*d)) == (Tan[vb]*
(Cos[vc]/d)) ==(Sin[vb]*(Cos[vd]/d)), Tan[vc] == (Tan[vc]*d)/d, Cos[vc] 
== d/(Cos[vc]/d),Tan[vd] == (Tan[vd]*d)/d, Cos[vd] == d/(Cos[vd]/d)}] 
//N

va = 17 Degree;
vb = 12 Degree;
d = 300;

Reduce[{
   Tan[va] == h/x,
   Tan[vb] == h/Sqrt[d^2 - x^2]}] // N