Answer
$39.2m$
Work Step by Step
Step 1. We use the figure as shown for the geometry, where T is the top of the tower, A is the end of the wire on the ground, B is the bottom of the tower.
Step 2. In the right triangle of TAC, we have $\angle ATC=90-58=32^\circ$
Step 3. In the triangle of TAB, use the Sine Law, we have $\frac{TB}{sin12^\circ}=\frac{100}{sin32^\circ}$. Thus the height of the tower is TB=$100\times\frac{sin12^\circ}{sin32^\circ}\approx39.2m$
