is it possible to have a right triangle in which the sine of one of the angles is equal to the cosine of one of the angles? why?

Yes, it is possible (see the explanation)

Step-by-step explanation:

we know that

In a right triangle, we have two complementary angles (their sum equal to 90 degrees)

so

If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa

Example

Suppose we have the right triangle ABC

The measure of angle C is 90 degrees

A and B are complementary angles

A+B=90°

therefore

sin (A) = cos (B)

sin (B) = cos (A)