The Longest Side

Part of the Triangles section of Coddy's Geometry journey. Lesson 5 of 63.

In any triangle, the biggest angle faces the longest side, and the smallest angle faces the shortest side. Picture opening a pair of scissors: the wider the angle between two sides, the farther apart their ends, so the longer the side across from it.

$Triangle PQR with 30 degrees at P and 70 degrees at Q$

Here the angles at P and Q are 30° and 70°, so the angle at R is 180 - 30 - 70 = 80 degrees, the biggest. The longest side is the one facing R: PQ. The shortest side faces the 30° angle at P: QR.

It works the other way too: the longest side always faces the biggest angle. In a right triangle the 90° angle is the biggest, so the side facing it is the longest. That side gets its own name later in this section.

Challenge

△ABC shows two of its angles. Work out the third angle, then tap the longest side and press Check. Go by the angles, not by how long the sides look.

Try it yourself

$Find the right part on the figure$