What is the angle of elevation of the sun when a 42 ft mast casts a 17 ft shadow

68.0°

Step-by-step explanation:

The tangent function relates the sides of a right triangle to the angle:

Tan = Opposite/Adjacent

The mast is opposite the angle of elevation, and the shadow is adjacent, so you have ...

tan (angle) = (42 ft) / (17 ft)

The inverse tangent function is used to find the angle whose tangent is a particular value.

angle = arctan (42/17) ≈ 67.964°

The angle of elevation is about 68.0°.