3.48: Triangle with surds; GP terms

Triangle $ABC$ has sides $AB=\sqrt{5}-1$, $AC=\sqrt{5}+1$ and $BC=x$, and area $\dfrac{2\sqrt{5}}{3}$. Angle $A$ is acute. Find the exact value of $\mathrm{sin}\,A$.

Find exact $\cos A$ and hence exact $x$.

Find exact $\sin B$.

A GP has third term $4.5$ and sixth term $15.1875$. Find $a$ and $r$.

Find the sum of ten terms starting with the sixteenth, to the nearest integer.