A 10-meter telephone pole casts a shadow directly down a slope when the angle of elevation of the sun is 42 degrees.
Find theta, the angle of elevation of the ground.
Remember that the sum of three angles in a triangle is $\displaystyle 180^{\circ}$.
Provided that the telephone pole is perpendicular to the ground (as all are), then $\displaystyle 90^{\circ} + 42^{\circ} + \theta ^{\circ} = 180^{\circ}$.
$\displaystyle 132^{\circ} + \theta ^{\circ} = 180^{\circ}$
$\displaystyle \theta ^{\circ} = 48^{\circ}$.
I believe the mistaken assumption was that the angle of elevation was angle between the top of the telephone poll and the shadow being cast. The angle of elevation for the sun is going to be the angle between the ground and the sun. Further, the telephone poll appears to be casting a shadow down a hill, not across a plane. The question is asking for the angle of elevation for the hill.