Determine the unknown angle

Question

For this question I'm a bit confused and don't know where to start by solving it, any guidance is appreciated.

Answer 1

First argue that all three rectangular triangles in the picture are similar. This means that the angle $\theta$ occurs in several places.

Then use trigonometry to define $\theta$ in terms of the sides of a convenient rectangular triangle.

Answer 2

Hypotenuse $ = \dfrac{8^2}{5} = 12.8 $

$$ \sin \theta = \frac{8}{12.8}. $$