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.
As you know that $AH=6$ and $\triangle ABC\equiv\triangle OBC$, so you have $OH=6$.
Now, apply Cosine Rule in $\triangle AOH$ given that $AO=4$ since the angle between the planes $ABC$ and $OBC$ is $\angle OHA$.