Answer
$48.2^\circ$
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where T is the top of the tower, Q is the bottom of the tower, P is the point on the hill. We are given $TQ=30m, PQ=120m, \angle TPQ=8^\circ$
Step 2. In triangle TPQ, use the Law of Sines, we have $\frac{sin\angle PTQ}{120}=\frac{sin8^\circ}{30}$ thus
$sin\angle PTQ=0.557$ and $\angle PTQ=sin^{-1}0.557\approx33.8^\circ$
Step 3. In the right triangle of TPR, $\angle TPR=90-33.8=56.2^\circ$ thus the angle of inclination of the hill is
$\angle QPR=56.2-8=48.2^\circ$
