Answer:
66°59'57.4379"
Step-by-step explanation:
A suitable calculator can find the angle whose sine is 0.9205 and convert that angle to degrees, minutes, and seconds
θ = arcsin(0.9205) ≈ 66.999288° ≈ 66°59'57.4379"
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Multiplying the fractional part of the degree measure by 60 minutes per degree gives the minutes measure:
0.999288° ≈ 59.95730'
And multiplying the fractional part of that by 60 seconds per minute gives the seconds measure:
0.95730' = 57.4379"
In total, we have 66°59'57.4379"
