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enter image description here

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

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

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

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

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