[math]\LARGE \begin{eqnarray}[br]\sin(\alpha)=\frac a c & \left (= \frac{\text{opposite}}{\text{hypotenuse}}\right )\\[br]\cos(\alpha)=\frac b c & \left (= \frac{\text{adjacent}}{\text{hypotenuse}}\right )\\[br]\tan(\alpha)=\frac a b & \left (= \frac{\text{opposite}}{\text{adjacent}}\right )\\[br]\end{eqnarray}[br][/math][br]

Trigonometric basic formulas help in solving the angle of an right-angled triangle. These basic formulas given you above.   [br][br][br][br][br][color=#3366ff][b]Example 2[/b][/color]. [i]The hypotenuse of a right-angled triangle is 398 and one of the acute angles is  76.4°. Define the legs.[/i][br][br]

The opposite leg can be solved with sine as [br][br]    [math]\Large \sin(76.4\degree)=\frac{y}{398} \;\;\Leftrightarrow\;\; y=398\cdot \sin(76.4\degree)\approx387[/math][br][br]The adjacent leg can be solved with cosine: [br][br]  [math]\Large \cos(76.4\degree)=\frac{x}{398} \;\;\Leftrightarrow\;\; x=398\cdot \cos(76.4\degree)\approx 94[/math][br]     [br][br][br][br][color=#3366ff][b]Example 3.[/b][/color] We knew the fix point and the distance from the pole in the example 1. It is easy to solve the angle between the guy wire and the ground with this information.[br][br]  [math]\Large \tan(\alpha)=\frac{3.2}{2.6} \;\;\Leftrightarrow\;\; \alpha=\tan^{-1}\left (\frac{3.2}{2.6} \right )\approx \tan^{-1}(1.23)= 50.9\degree[/math][br]