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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: $\boxed{2\sqrt{61}}$. 📰 401K Conversion To Roth Ira 8350588 📰 Hhs Ocr 2025 November Update Breaking Policies That Will Shake The Nation 3196060 📰 New Ids 9621525 📰 Crema Para Quemaduras 5155582 📰 Bat With Sparkling Wings Surprised The Worldyou Wont Believe What Happened Next 7869351 📰 The Ultimate Solitaire Engagement Ring That Transformed Wedding Waiting Into Thrilling Adventure 3602790 📰 Android Data Recovery Mac 3678170 📰 Jonathan Nolan 898394 📰 Mechanic Salary 9728176 📰 Govx Ticker Crushed Expectations Heres The Shocking Surge That Shocked Investors 328275 📰 Tv Series Wipeout 866061 📰 The Truth About Tucsons Best Kept Secrets No Guide Ever Spoke 1069500 📰 How To Point In Gta 5 4014498 📰 Universe Football 8251818 📰 Discover Why Rhode Sparks Before Every Party In Secret Shine 6080770