Answer:
approximately 57 degrees (when rounded off from 56.59 degrees)
Explanation:
Imagine a right triangle with the 90 degree (right) angle at the foot of the mast. The sun, striking the mast, casts a 31 ft shadow. Think of this shadow as lying on the "adjacent side" of the angle of elevation, and the height of the mask on the "opposite side."
The trig function "tangent" includes the variables in question:
tan (angle of elevation) = (opposite side) / (adjacent side).
Then, in this particular case, tan (angle of elevation) = opp side / adj side
takes is
tan (angle of elevation) = 47/31 = 1.516 = 0.9877 radians, or
0.9877 rad 180 deg
----------------- * ------------- = 56.59 deg, or approximately 56.6 deg, or
1 π rad approximately 57 deg