Question

What formula should I be using to find tangent of the road length?

Answer 1

In general, the intersecting secant-tangent theorem states that

Then,

$DC^2=BC*AC$

Therefore, in our case,

$\begin{gathered} \Rightarrow DC^2=AC*BC=\left(AB+BC\right)*BC=\left(10+15\right)*15 \\ \Rightarrow DC^2=25*15=375 \\ \Rightarrow DC=\sqrt{375}=5\sqrt{15}=19.3649... \end{gathered}$

The exact answer is DC=5sqrt(15)