# Thread: Find Hypotenuse when given two angles and side

1. ## Find Hypotenuse when given two angles and side

Hello. I was hoping someone would be able to help with this problem I have.

I have a right triangle. I need to find the hypotenuse x.

I am given the opposite side of 20 and the θ of 32 degrees. How do I find the hypotenuse with all this?

If you would be able to explain how you got the answer, I would really appreciate it. I know this work isn't going anywhere anytime soon so I would really like to learn how to do this for future reference. Thank you so much guys.

2. ## Re: Find Hypotenuse when given two angles and side

In a right triangle, an acute angle is $\displaystyle 32^o$ and the opposite side has length $\displaystyle 20.$
Find the length of the hypotenuse.

Code:
      *
*   *
opp *       *    hyp
20 *           * x
*               *
*             32o   *
*  *  *  *  *  *  *  *  *
adj
We know that: .$\displaystyle \sin\theta \:=\:\frac{opp}{hyp}$

So we have: .$\displaystyle \sin32^o \:=\:\frac{20}{x}$

Hence: .$\displaystyle x \;=\;\frac{20}{\sin32^o} \;=\;37.7415983$

Therefore: .$\displaystyle x \;\approx\;37.7$

3. ## Re: Find Hypotenuse when given two angles and side

Thank you so much. Great answer.