Solution:
Given:
Applying the Pythagorean theorem to the right triangle,
[tex]\begin{gathered} \text{hypotenuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ \text{where;} \\ \text{hypotenuse}=18m \\ \text{adjacent}=10m \\ \text{opposite}=h \\ \\ \text{Hence,} \\ 18^2=h^2+10^2 \\ h^2+10^2=18^2 \end{gathered}[/tex]
Thus,
[tex]h^2+10^2=18^2[/tex][tex]\begin{gathered} h^2+10^2=18^2 \\ h^2+100=324 \\ h^2=324-100 \\ h^2=224 \\ h=\sqrt[]{224} \\ h=14.97m \end{gathered}[/tex]
Therefore, the value of the height of the ladder, h = 14.97m
