Question

A 2.7 meter ladder leans against a house forming a 30° angle with the house. Exactly how far is the base of the ladder from the house?

Answer 1

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:

`\begin{gathered} \sin (30)=\frac{\text{opposite side}}{hypotenuse}=(x)/(2.7) \\ \Rightarrow(1)/(2)=(x)/(2.7) \\ \Rightarrow x=2.7\cdot(1)/(2)=1.35 \\ x=1.35 \end{gathered}`

thus, the base of the ladder is 1.35m from the house