A vertical tower stands on a hill with an angle of elevation of $\displaystyle {5.3}^{\circ}$.  At a point $\displaystyle {30.1}$ $\displaystyle {m}$ down the hill from the tower, the angle of elevation to the top of the tower is $\displaystyle {17.8}^{\circ}$. How tall is the tower to the nearest tenth of a meter?