1. The problem states that in a spherical triangle, the angles are given as $A=90^\circ$, $B=100^\circ$, and $C=92^\circ$. 2. We need to determine which rule is used to solve a spherical triangle with these given angles. 3. In spherical trigonometry, the main rules are the Sine Rule, Cosine Rule, Napier's Rule (for right spherical triangles), and the Pythagorean theorem (only for plane right triangles). 4. Since angle $A=90^\circ$, the triangle is a right spherical triangle. 5. Napier's Rule is specifically designed for right spherical triangles and relates the sides and angles in such triangles. 6. Therefore, the correct rule to use here is Napier's Rule. Final answer: Napier's Rule