Trigonometry

In order to calculate forces, vectors and angles, we use trigonometry. These are the mathematical operators for inspecting a triangle by means of the three sides and the three angles. The side opposite to the 90° angle is called hypotenuse. The other two sides are the adjacent side (referring to α or β), and the opposite side.
$\cos \left(\mathrm{(\alpha )}\right)=\frac{\mathrm{b}}{\mathrm{c}}$ $\sin \left(\mathrm{(\alpha )}\right)=\frac{\mathrm{a}}{\mathrm{c}}$ $\tan \left(\mathrm{(\alpha )}\right)=\frac{\mathrm{b}}{\mathrm{a}}$

Side missing

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Given: α = 30°, a = 10
Searched: x

Solution: Set up the trigonometric formula and then rearrange it for the desired quantity
$\tan \left(\mathrm{(30°)}\right)=\frac{\mathrm{10}}{\mathrm{x}}$ $\leftrightarrow \mathrm{x}=\frac{10}{\tan \left(\mathrm{(30°)}\right)}\approx 17.32$

Angle missing

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Given: c = 5, a = 3
Searched: α

Solution: Set up the trigonometric formula and then rearrange it for the desired quantity
$\sin \left(\mathrm{(\alpha )}\right)=\frac{\mathrm{3}}{\mathrm{5}}$ $\leftrightarrow \mathrm{\alpha }={\sin }^{-1}\left(\frac{3}{5}\right)\approx 36.9°$