# Determine the unknown angle

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

• Can you find the angle at the very top of the figure? – user296602 Dec 16 '15 at 21:54
• What is the question? – Justpassingby Dec 16 '15 at 21:54
• Have you learnt about the $\cos$ and $\sin$ functions yet? – 5xum Dec 16 '15 at 21:55
• The trick is to use the fact that all angles in a triangle sum up to 180°. – FlyingDutchman Dec 16 '15 at 21:55
• Notice, in right triangle having perpendicular $5$ & hypotenuse $8$, hence $$\sin\theta=\frac{5}{8}\implies \theta=\sin^{-1}\frac{5}{8}=38.68^\circ$$ – Harish Chandra Rajpoot Dec 16 '15 at 22:24

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.
Hypotenuse $= \dfrac{8^2}{5} = 12.8$
$$\sin \theta = \frac{8}{12.8}.$$