Assume that the Earth is a perfect sphere.  A plane flies between $30^\circ$ N $45^\circ$ W and $30^\circ$ N $45^\circ$ E along the shortest possible route along the surface of the Earth.  Let $\theta$ be the northernmost latitude that the plane flies over.  Compute $\sin \theta.$
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<|im_start|>user
Assume that the Earth is a perfect sphere.  A plane flies between $30^\circ$ N $45^\circ$ W and $30^\circ$ N $45^\circ$ E along the shortest possible route along the surface of the Earth.  Let $\theta$ be the northernmost latitude that the plane flies over.  Compute $\sin \theta.$
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<|im_start|>assistant

user
\frac{\sqrt{10}}{5}
Assume that the Earth is a perfect sphere.  A plane flies between $30^\circ$ N $45^\circ$ W and $30^\circ$ N $45^\circ$ E along the shortest possible route along the surface of the Earth.  Let $\theta$ be the northernmost latitude that the plane flies over.  Compute $\sin \theta.$
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