A ladder of length \(\text{15}\) \(\text{m}\) is resting against a wall, the base of the ladder is \(\text{5}\) \(\text{m}\) from the wall. Find the angle between the wall and the ladder.

First draw a sketch:

Notice that we want to find the angle that the ladder makes with the wall, not the angle that the ladder makes with the ground.

Now we use \(\sin x = \frac{\text{opposite}}{\text{hypotenuse}}\):

\begin{align*} \sin x & = \frac{5}{15} \\ & = \text{0,3333...} \\ x & = \text{19,4712...} \\ & \approx \text{19,47}° \end{align*}The angle between the ladder and the wall is \(\text{19,47}\)°.