82 meters
Explanation
Step 1
Draw:
as the angle of the sun´s ligth is the same for both, we have two congruent trianges, then we can make a proportion
[tex]\text{ratio}=\frac{heigth}{\text{shadow}}[/tex]so
[tex]\begin{gathered} \text{ratio}_1=ratio2 \\ \text{replacing} \\ \frac{3.1}{1.46}=\frac{x}{38.5} \\ to\text{ solve, multiply both sides by 38.5} \\ \frac{3.1}{1.46}\cdot38.5=\frac{x}{38.5}\cdot38.5 \\ 81.74\text{ m=x} \\ \text{rounded} \\ x=82 \end{gathered}[/tex]therefore, the heigth of the tower is
82 meters
