Question

Hello there I need help with this question please make it easy to understand

Answer 1

Given figure:

To find AC:

Consider the right triangle ABE,

$\begin{gathered} AB^2=AE^2+BE^2 \\ 13^2=3^2+BE^2 \\ 169=9+BE^2 \\ BE^2=169-9 \\ BE^2=160 \\ BE=\sqrt[]{160} \\ \text{That is, BE=CD=}\sqrt[]{160} \end{gathered}$

Next, consider the right triangle ACD,

$\begin{gathered} AC^2=CD^2+AD^2 \\ AC^2=(\sqrt[]{160})^2_{}+10^2 \\ AC^2=160+100 \\ AC^2=260 \\ AC=\sqrt[]{260} \\ AC\approx16.1 \end{gathered}$

Thus, the answer is 16.1 cm.