Find θ in degrees, minutes and second, given: sin θ = 0.9205

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"