Naming the Sides of a Right Triangle: Hypotenuse, Opposite, Adjacent

0:00Each side of a right triangle has its own name. Which side is which?

0:05The small square at C marks the right angle, which is exactly 90 degrees.

0:11Our triangle has sides of 3 centimetres, 4 centimetres and 5 centimetres.

0:18Check: 3 squared plus 4 squared is 9 plus 16, which is 25, and 5 squared is also 25.

0:28The hypotenuse is the side across from the right angle. It is always the longest side, here 5 centimetres.

0:36Now pick one of the other two angles and mark it with theta, a Greek letter used for angles.

0:42The opposite side is across from theta. It does not touch theta at all.

0:48Adjacent means next to. The adjacent side touches theta and is not the hypotenuse.

0:55Careful: the hypotenuse touches theta too, but it is never called the adjacent side.

1:03So with theta at A, opposite is 3 centimetres, adjacent is 4 centimetres and the hypotenuse is 5 centimetres.

1:13Now move theta to the other corner, at B.

1:17Opposite and adjacent swap. The 4 centimetre side is now across from theta, and the 3 centimetre side touches it.

1:25With theta at B, opposite is 4 centimetres, adjacent is 3 centimetres and the hypotenuse is still 5 centimetres.

1:35The hypotenuse stays across from the right angle, and theta names the other two sides: opposite and adjacent.