Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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:

Triangle with one side and three angles

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)?

share|improve this question
    
according to the formula $c\cdot\cos 30 = a$ –  W_D Sep 4 '13 at 12:41
add comment

1 Answer

up vote 1 down vote accepted

just use Law of sines (https://en.wikipedia.org/wiki/Law_of_sines): it states that

$$\frac{a}{\sin{\alpha}} = \frac{b}{\sin{\beta}} = \frac{c}{\sin{\gamma}}$$

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 $c = \frac{a}{\sin{60°}}$.

share|improve this answer
    
Thanks a lot. Exactly what I needed. Who knew it would be so simple :) –  Trenskow Sep 4 '13 at 13:05
1  
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
    
if you have a nail to pe put on a wall, everything is a hammer :-) –  mau Sep 5 '13 at 7:04
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.