In triangle ABC, when we refer to it as a right triangle, we’re acknowledging that one of its angles is a right angle, which measures 90 degrees. By definition, a right triangle has one angle that is exactly 90 degrees, and the other two angles must be acute angles, meaning they are less than 90 degrees.
In this case, let’s designate angle C as the right angle (90 degrees). Consequently, this leaves angles A and B to share the remaining 90 degrees because the sum of all angles in a triangle is always 180 degrees.
The key relationship between angles A and B can be expressed mathematically as:
A + B = 90 degrees
This means that angle A and angle B are complementary angles. If angle A increases, angle B must decrease accordingly to maintain that sum of 90 degrees, and vice versa. Therefore, for any right triangle ABC, whenever you know one of the acute angles (either A or B), you can easily determine the other angle using this relationship.
For instance, if angle A measures 30 degrees, angle B must measure 60 degrees (since 30 + 60 = 90). This relationship between the two acute angles not only holds true for triangle ABC but is a fundamental property of all right triangles.