Find the missing angle and side of the top right triangle.

Let's analyze the bottom right triangle OPS, where side OP is 4.2, side OS is 8.4, and angle P is 90 degrees. We need to find the angle O and the length of side PS. First, let's find the angle O. We can use the sine function: $$\sin(O) = \frac{PS}{OS}$$ We don't know PS yet, so let's find the length of side PS using Pythagorean theorem: $$OS^2 = OP^2 + PS^2$$ $$8.4^2 = 4.2^2 + PS^2$$ $$70.56 = 17.64 + PS^2$$ $$PS^2 = 70.56 - 17.64$$ $$PS^2 = 52.92$$ $$PS = \sqrt{52.92} = 4.2\sqrt{3}$$ Now, we can find the angle O. We can use the tangent function: $$\tan(O) = \frac{PS}{OP} = \frac{4.2\sqrt{3}}{4.2}$$ $$\tan(O) = \sqrt{3}$$ $$O = \arctan(\sqrt{3}) = 60^{\circ}$$ Answer: Angle O is $$60^{\circ}$$ and PS = $$4.2\sqrt{3}$$