# Length of hypotenuse using one side length and angle

I bet this question has been asked a million times, but I can't find a straight answer. I need to find the length of the hypotenuse in a triangle where I have one side and all the angles.

Example:

Now in the above triangle I have the length of a = 20 and all the angles. How do I - from here - get the length of the hypotenuse (c)?

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according to the formula $c\cdot\cos 30 = a$ –  W_D Sep 4 '13 at 12:41

$$\frac{a}{\sin{\alpha}} = \frac{b}{\sin{\beta}} = \frac{c}{\sin{\gamma}}$$
where $\alpha, \beta, \gamma$ are the angles opposited to sides $a, b, c$ respectively. Since $\gamma$ is a right angle, $\sin{\gamma} = 1$, and therefore in your example $c = \frac{a}{\sin{60°}}$.
This is shooting an ant with a cannon! Just use the right-angle definitions of $\sin$ and $\cos$, as an earlier comment suggested. $a/c = \text{opposite/hypotenuse}=\sin 60^\circ$. –  Ted Shifrin Sep 4 '13 at 15:02