Answer:
![B \approx 32.1\°; A \approx 39.0\°](https://tex.z-dn.net/?f=B%20%5Capprox%2032.1%5C%C2%B0%3B%20A%20%5Capprox%2039.0%5C%C2%B0)
Step-by-step explanation:
Sine theorem: in any triangle, the ratio between a side and the sine of the opposite angle is constant
![\frac{sin\ \alpha}a = \frac{sin\ \beta}b =\frac{sin\ \gamma}c](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5C%20%5Calpha%7Da%20%3D%20%5Cfrac%7Bsin%5C%20%5Cbeta%7Db%20%3D%5Cfrac%7Bsin%5C%20%5Cgamma%7Dc)
In our case, for the left triangle,
![\frac {sin\ 103\°}{11} =\frac{sin\ B} 6 \rightarrow sin\ B = \frac6{11} sin\ 103\°](https://tex.z-dn.net/?f=%5Cfrac%20%7Bsin%5C%20103%5C%C2%B0%7D%7B11%7D%20%3D%5Cfrac%7Bsin%5C%20B%7D%206%20%5Crightarrow%20sin%5C%20B%20%3D%20%5Cfrac6%7B11%7D%20sin%5C%20103%5C%C2%B0)
Time to grab a calculator and crunch numbers. Double check your calculator is in degrees and not in radians (plug in sin 30°, if you're getting 0.5 you're good) and you will get
![sin\ B \approx 0.53 \rightarrow B \approx 32.1\°](https://tex.z-dn.net/?f=sin%5C%20B%20%5Capprox%200.53%20%5Crightarrow%20B%20%5Capprox%2032.1%5C%C2%B0)
Same difference with the right triangle. With the same calculations
![sin\ A = \frac{26}{41} sin 83\° \approx 0.68 \rightarrow A \approx 39.0\°](https://tex.z-dn.net/?f=sin%5C%20A%20%3D%20%5Cfrac%7B26%7D%7B41%7D%20sin%2083%5C%C2%B0%20%5Capprox%200.68%20%5Crightarrow%20A%20%5Capprox%2039.0%5C%C2%B0)