<s>[INST] Fairly simple trig question Three points at coordinates $(0,c)$, $(p,q)$, $(0,d)$ respectively. The angle at $(p,q)$ between $(0,c)$ and $(0,d)$ is $θ$. Find $d$.

P.s. This isn't homework.
 [/INST] Hint :
Let $A(0,c)$, $B(0,d)$, and $C(p,q)$. Length $AB=c-d$,
\begin{align}
AC^2=p^2+(c-q)^2
\end{align}
and
\begin{align}
BC^2=p^2+(q-d)^2
\end{align}
Using cosine formula, we get
\begin{align}
AB^2&=AC^2+BC^2-2\cdot AC\cdot AB\cos\theta\\
(c-d)^2&=p^2+(c-q)^2+p^2+(q-d)^2-2\sqrt{(p^2+(q-d)^2)(p^2+(q-d)^2)}\cos\theta\\
\end{align}
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