To solve the right spherical triangle $ACB$ with the provided information, we can use formulas from spherical trigonometry for right triangles. In a right spherical triangle, when one of the angles is $90^\circ$ (as is $C$ in this case), we can use specific relationships involving the remaining angles and sides.

Given dataTo solve the right spherical triangle $ACB$ with the provided information, we can use formulas from spherical trigonometry for right triangles. In a right spherical triangle, when one of the angles is $90^\circ$ (as is $C$ in this case), we can use specific relationships involving the remaining angles and sides.

Given

• $C = 90^\circ$
• $A = 48^\circ 26'$
• $B = 110^\circ 40'$
• $a = 44^\circ 50'$
• $b = 118^\circ 09'$
• $c = 109^\circ 33'$

Let's proceed with solving for unknowns if there are any, or verifying the information using spherical trigonometric identities. The most useful formulas for a right spherical triangle $ABC$ are:

1. Sine Rule for sides and angles: $\sin a = \sin A \cdot \sin c$ $\sin b = \sin B \cdot \sin c$

2. Cosine Rule for sides: $\cos c = \cos a \cdot \cos b$

3. Cosine Rule for angles: $\cos C = \cot A \cdot \cot B$

Since angle $C$ is already known to be $90^\circ$, the calculation becomes somewhat simpler, and we can check for consistency using these relationships.

Would you like me to go through the step-by-step verification of each part using these formulas?

Here are some related questions to expand understanding:

1. What is the sine rule in spherical trigonometry, and how does it differ from the planar version?
2. How do cosine rules for spherical triangles apply when one angle is $90^\circ$?
3. What are Napier's analogies, and how can they be applied to spherical triangles?
4. Why are spherical triangles useful in navigation and astronomy?
5. How would the solution change if none of the angles were $90^\circ$?

Tip: In spherical trigonometry, remembering that angles and sides are measured in angles (not distances) is key, as it differentiates it fundamentally from planar geometry.