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Answer:
1. First, convert the angles from minutes (') to radians. Remember that 1 degree = 60 minutes and 1 radian ≈ 57.2958 degrees.
[tex]a = 75' = 75/60 = 1.25 degrees = 1.25 * (π/180) radians ≈ 0.0218 radians
[/tex]
[tex]b = 64' = 64/60 = 1.0667 degrees = 1.0667 * (π/180) radians ≈ 0.0186 radians
[/tex]
[tex]c = 90' = 90/60 = 1.5 degrees = 1.5 * (π/180) radians ≈ 0.0262 radians
[/tex]
2. Now, we can use the Sine Rule for Spherical Triangles to solve for the remaining parts of the triangle. The Sine Rule states:
[tex]sin(A)/sin(a) = sin(B)/sin(b) = sin(C)/sin(c)[/tex]
Let's calculate the values using the given information:
[tex]sin(A)/sin(0.0218) = sin(B)/sin(0.0186) = sin(C)/sin(0.0262)[/tex]
3. Solve the equation using the Sine Rule to find the angles A, B, and C of the spherical triangle. You can use trigonometric functions to find the values.
Once you have the values for A, B, and C, you will have solved for the spherical triangle with parts a = 75', b = 64', and c = 90'. If you need further assistance with the calculations, feel free to ask!