Question

Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.

Answer 1

Answer:

67 and 23..................

Answer 2

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:

$\frac{13}{sin90^o}= \frac{12}{sin \alpha } \ \ \to \ \ sin \alpha = \frac{12 \cdot sin90^o}{13}= \frac{12*1}{13} \approx 0.923 \ \ \to \ m\angle \alpha \approx 67^o$

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).