The sine of an angle is $0.6$, find the two possible values for angle.

1. Find the acute angle whose sine is $0.6$.

$\sin \theta = 0.6$

$\theta = \sin^{-1}(0.6) = 36.869\ldots^\circ$

2. Find the second possible angle where sine is positive.

Since sine is positive in the first and second quadrants,

second angle $= 180^\circ - 36.869\ldots^\circ = 143.130\ldots^\circ$.

So the two possible angles are $36.9^\circ$ and $143.1^\circ$, correct to 1 decimal place.