Regarding the tetrahedron OABC in the picture, with sides $BC=10$, $AC=8$, $OA=4$, $\sin(\angle ACB)=\frac{3}{4}$ and $\triangle ABC \equiv \triangle OBC$. With this, you find that the area of $\triangle ABC=30$.

Moreover, if $AH$ denotes the perpendicular line drawn from point $A$ to side $BC$, you can find its value is $6$.

Now, to the questions:

Since $\triangle ABC$ and $\triangle OBC$ have a common side, all their sides have the same values, right?

Let $\theta$ denote the angle formed by the plane $ABC$ and the plane $OBC$. How do I find $\cos \theta$ and $\sin\theta$?

And at last, how do I find the the volume?

I need help on how to visualize these concepts.