word problem

Note that  the sine of an angle  is just  opposite side / hypotenuse

Here.....the opposite side  = 11.8  and the hypotenuse  =12

So...we need to use the sine inverse  (arcsin) function to determine the angle this makes with the ground

arcsin ( 11.8 / 12)  =  angle measure  =  79.5°

So....the ladder is not safe with this angle

Here's a pic :