Solution:
Given that an 18-foot ladder leans against a wall so that the base of the ladder is 10 feet from the base of the building, we can illustrate this in a diagram as shown below:
where
[tex]\begin{gathered} FT\Rightarrow length\text{ of the ladder} \\ FB\Rightarrow distance\text{ from the base of the ladder to the wall} \\ \theta\Rightarrow angle\text{ the ladder makes with the building} \end{gathered}[/tex]To evaluate the angle the ladder makes with the building, we use trigonometric ratio.
From trigonometric ratios:
[tex]\sin\theta=\frac{opposite}{hypotenuse}[/tex]In this case,
[tex]\begin{gathered} opposite\Rightarrow FB \\ hypotenuse\Rightarrow FT \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} \sin\theta=\frac{FB}{FT} \\ =\frac{10}{18} \\ \Rightarrow\sin\theta=0.5555555556 \\ \end{gathered}[/tex]Take the sine inverse of both sides,
[tex]\begin{gathered} \sin^{-1}(\sin\theta)=\sin^{-1}(0.5555555556) \\ \Rightarrow\theta=33.7489886\degree \end{gathered}[/tex]Hence, the angle the ladder makes with the building is
[tex]\begin{equation*} 33.7489886\degree \end{equation*}[/tex]
