25 ft
Explanation
as the mirror is on the ground totally hoziontal , the angle is the same for both triangles,hence, the triangles are congruent, so we can set a proportion
Step 1
set the proportion
let
[tex]\text{ratio}=\frac{heigth}{\text{below side}}[/tex]replace
[tex]\begin{gathered} \text{ratio}_1=\frac{5}{7.7} \\ \text{ratio}_2=\frac{heigth\text{ of the tr}e(T)}{39} \end{gathered}[/tex]the triangles are congruent, so
[tex]\begin{gathered} \text{ratio}_1=ratio_2 \\ \frac{5}{7.7}=\frac{T}{39}\rightarrow proportion \end{gathered}[/tex]Step 2
solve the equation
[tex]\begin{gathered} \frac{5}{7.7}=\frac{T}{39} \\ \text{Multiply both sides by 39} \\ \frac{5}{7.7}\cdot39=\frac{T}{39}\cdot39 \\ 25.32=T \\ \text{rounded} \\ T=25\text{ ft} \end{gathered}[/tex]so, the answer is
25 ft
I hope this helps you