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📰 Solution: Divide both sides by 2: $\sin(2z) = \frac{\sqrt{3}}{2}$. The general solutions for $2z$ are $2z = 60^\circ + 360^\circ k$ or $2z = 120^\circ + 360^\circ k$, where $k$ is an integer. Solve for $z$: $z = 30^\circ + 180^\circ k$ or $z = 60^\circ + 180^\circ k$. Within $[0^\circ, 360^\circ]$, valid solutions are $z = 30^\circ, 60^\circ, 210^\circ, 240^\circ$. Final answer: $\boxed{30^\circ, 60^\circ, 210^\circ, 240^\circ}$. 📰 Question: In a city grid, $\|\overrightarrow{OA}\| = 5$ km and $\|\overrightarrow{OB}\| = 12$ km, with an angle of $90^\circ$ between them. If $\overrightarrow{OC} = 2\overrightarrow{OA} - \overrightarrow{OB}$, find $\|\overrightarrow{OC}\|$. 📰 Solution: Use the Pythagorean theorem since $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are perpendicular. Compute $\|\overrightarrow{OC}\|^2 = (2\|\overrightarrow{OA}\|)^2 + (\|\overrightarrow{OB}\|)^2 = 4(25) + 144 = 100 + 144 = 244$. Thus, $\|\overrightarrow{OC}\| = \sqrt{244} = 2\sqrt{61}$. Final answer: $\boxed{2\sqrt{61}}$. 📰 Tzdata Mystique How This Resource Can Transform Your Data Game Overnight 4680684 📰 Why Not All Those Who Wander Are Lost Is The Courageous Truth Everyones Missing Online 6560951 📰 What Does Yh Mean 565105 📰 Shocking Facts About Vgk Etf You Need To Know Before It Explodes 6494258 📰 Blistering Putt Putts Madness Level Up Your Game With This Simple Trick 2070341 📰 Games Gift Card 9246248 📰 How Much Caffeine Is In Dr Pepper 8286019 📰 Best Credit Cards 2656895 📰 Epic Subscription 2239014 📰 Slide Presentation Templates 6781618 📰 Jonathan Becker Police Impersonator 2268928 📰 Tablet Surface Pro 3109365 📰 Why Everyones Obsessed With Alexa Jeong The Truth You Need To Know 7014291 📰 This Horror Game Won Everyones Scaresyou Gotta Play To Survive 3837585 📰 Abused 5235730