In the right triangle, the longest side is the hypotenuse.
Let α be the angle opposite to the side with a length of 12 units, then according to the Law of sines:
[tex] \frac{13}{sin90^o}= \frac{12}{sin \alpha } \ \ \to \ \ sin \alpha = \frac{12 \cdot sin90^o}{13}= \frac{12*1}{13} \approx 0.923 \ \ \to \ m\angle \alpha \approx 67^o[/tex]
In a triangle, the three interior angles always add to 180° ⇒
third angle = 180 - 90 - 67 = 23°
Answer:
67° and 23° (to the nearest degree).
