First calculate the missing angle
![\alpha](https://tex.z-dn.net/?f=%5Calpha)
. By knowing all angles in triangle have a sum of 180°.
![\alpha=180-(\gamma+\beta)](https://tex.z-dn.net/?f=%5Calpha%3D180-%28%5Cgamma%2B%5Cbeta%29)
![\alpha=180-(90+49)=\boxed{41}](https://tex.z-dn.net/?f=%5Calpha%3D180-%2890%2B49%29%3D%5Cboxed%7B41%7D)
Now we required to use angle functions in a right triangle. The cosine of
![\beta](https://tex.z-dn.net/?f=%5Cbeta)
is equal to the relation of side
![a](https://tex.z-dn.net/?f=a)
and hypotenuse
![c](https://tex.z-dn.net/?f=c)
.
Now we solve this for hypotenuse.
![\cos(\beta)=\frac{a}{c}](https://tex.z-dn.net/?f=%5Ccos%28%5Cbeta%29%3D%5Cfrac%7Ba%7D%7Bc%7D)
![c=\frac{a}{\cos(\beta)}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7Ba%7D%7B%5Ccos%28%5Cbeta%29%7D)
Now put in the numbers.
![c=\frac{9}{\cos(49)}\approx\boxed{13.7}](https://tex.z-dn.net/?f=c%3D%5Cfrac%7B9%7D%7B%5Ccos%2849%29%7D%5Capprox%5Cboxed%7B13.7%7D)
So we know the length of hypotenuse and length of side
![a](https://tex.z-dn.net/?f=a)
therefore side
![b](https://tex.z-dn.net/?f=b)
can be calculated using Pythagorean theorem:
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
.
Solve for side
![b](https://tex.z-dn.net/?f=b)
.
![c^2=a^2+b^2](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2)
![b=\sqrt{c^2-a^2}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7Bc%5E2-a%5E2%7D)
![b=\sqrt{13.7^2-9^2}\approx\boxed{9.7}](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B13.7%5E2-9%5E2%7D%5Capprox%5Cboxed%7B9.7%7D)
So there you go. If you have any questions feel free to ask.
r3t40