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Right angled triangle

The longest side of a right anfgled triangle is called the hypotenuse.
Right triangle with hypotenuse

The other two sides are sometimes called the legs.

ABC Triangle

The vertices of a right angled triangle are usually named, so that the vertex with the right angle is called C (capital C).
The next vertex of the triangle (in clockwise direction) is called A, followed by the vertex B.

The side opposite A, is called a.
The side opposite B, is called b.
The side opposite C, is called c.

Vertices are usually named with capital letters, while sides are named with lower case letters.
The letters are not necessarily A, B and C. Sometimes you see triangles named with other letters:
Right triangles with other letters

The opposite side

The side a positioned opposite the vertex A, is called the opposite side to A, just like b is the opposite side to B.

The adjacent side

Adjacent means “being close to”. That is the side not opposite but next to the vertex. The side b is for example the adjacent side to A.