Answer
The distance across the lake, from point B to point C is approximately $20$ meters.
Work Step by Step
The question appears tricky but what we just needed to do is to use the distance formula in finding the length of the line formed by points B and C.
With respect to the reference point $A (0,0)$, point B has coordinates $(3,1)$ and point C has coordinates $(19,13)$.
So using the distance formula: $$\sqrt{((x_{2}−x_{1})^{2}+(y_{2}−y_{1})^{2})}$$
Hence for line AB we have: $x_{1} = 3$, $x_{2} = 19$, $y_{1} = 1$, $y_{2} = 13$
Substituting to the formula: $$\sqrt{((19−3)^{2}+(13−1)^{2})}$$ $$=\sqrt{((16)^{2}+(12)^{2})}$$ $$=\sqrt {(256+144)}$$ $$=\sqrt{400}$$ $$= 20$$
