Can this triangle be solved?

Question

I am struggling with this question. I am unsure if it can be solved or if there is a mistake in it. Specifically, $\angle ADC$ looks to be $90^\circ$ but is not marked as such. So, given that $\angle ADC$ is unknown, can this be solved using the sine or cosine rule? This is meant to be a GCSE level question and I am really struggling to see a simple solution. Thank you.

Answer 1

The only features of the diagram that are fixed is the triangle $\triangle ABC$. You can solve for all angle measures and all side lengths for this triangle. However, point $D$ relative to this triangle can be positioned at any location along the ray $BC$ such that $BC < BD$. Therefore, the length of $CD$ is not uniquely determined. An additional assumption is required but not stated.

Answer 2

Suppose AD is not joined as given and it is required to solve only the acute angled triangle part ABC:

$$\angle CBA = 47^{\circ};\;\angle CAB = 59-47=12^{\circ};AB=49\;; $$

This way it can be solved.