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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: $\boxed{2\sqrt{61}}$. 📰 Breakthroughs In Jdk Latest Supercharging Your Java Projects Now 5724867 📰 Bay Wheels The Ultimate Accessory That Ships In Flash Dont Miss Out 8831824 📰 Putt Putt Travels Through Time Computer Game 2633127 📰 Alien Run Exposed Chaos Unleashedwhat Happened Next Will Shock You 5602473 📰 Breaking Down The Office Of The Secretary Hhsthis Shocking Insight Will Change Everything 71732 📰 Childs Travel Bag 8836899 📰 From Illness To Revelation Lady Ks Bold Fight With The Sick Man Exposed 8520022 📰 The Shocking Truth About White Labradors You Didnt Know Buy Now 5022681 📰 The Shocking Secrets Behind Microsofts Corporate Holiday Season Revealed 5489727 📰 Rockwood Park Golf Course 9384539 📰 Flexor 3869408 📰 Bonnaroo Tickets 6222541 📰 Kelsey Mitchell Twin 5870746 📰 Pantheon Season 2 Shocked Us Allheres The Untold Secrets You Missed 7164150 📰 Stephen Hawking Net Worth Shock The Billionaire Legacy Behind The Theoretical Genius 9502623