I'm not sure whether it's correct or not. The answer is supposed to be in 0.1 - 0.9. And with your equation, the result excesses the range :(v^2/rg = [sin(23.9) + μ*cos(23.9)]/[cos(23.9) - μ*sin(23.9)]
using v = 25.33 m/s and r = 77 m, find v^2/rg. Substitute this value in the above equation and find μ. What is the expected answer?