Given the information, we have the following right triangle:
notice that x represents the distance from the base of the ladder to the house.
Then, using the trigonometric function sine we have the following:
[tex]\begin{gathered} \sin (30)=\frac{\text{opposite side}}{hypotenuse}=\frac{x}{2.7} \\ \Rightarrow\frac{1}{2}=\frac{x}{2.7} \\ \Rightarrow x=2.7\cdot\frac{1}{2}=1.35 \\ x=1.35 \end{gathered}[/tex]thus, the base of the ladder is 1.35m from the house
