How can I find ∠ADC?

Question

Here is the picture:

v=16 and w=25 and d is the angle of reference. I have to find ∠ADC.

Here is what I have done:

$\frac {sin(∠adc)}{25}$=$\frac {sin(30)} {16}$

sin(∠adc)=$\frac {25sin(30)} {16}$

∠adc=arcsin($\frac {25sin(30)} {16}$)

∠adc = 51.4

which means that ∠ADC=51.4. It is pretty obvious that it is incorrect because of the look of the angle. What did I do wrong and how do I find the right answer?

Answer 1

If $0\leq a\leq 1$ the equation: $$\sin x = a$$ has two solutions in $[0,\pi]$, namely $x_1 = \arcsin a$ and $x_2 = \pi -x_1$.

Answer 2

It might be easier to understand with this Wikipedia explanation:

https://en.wikipedia.org/wiki/Law_of_sines#The_ambiguous_case_of_triangle_solution