Hypotenuse

The longest side of a right-angled triangle, opposite the right angle. CAPS Grade 9 definition, worked example and related geometry practice.

The longest side of a right-angled triangle, opposite the right angle.

Definition

The hypotenuse is the side opposite the right angle in a right-angled triangle. It is always the longest side, and in the Theorem of Pythagoras it is the c in c² = a² + b².

Worked example

A right-angled triangle with shorter sides 6 cm and 8 cm has hypotenuse √(36 + 64) = 10 cm.

If the hypotenuse is 13 cm and one side is 5 cm, the third side is √(169 − 25) = 12 cm.

Where it appears in the exam

Hypotenuse is part of the geometry section of CAPS Grade 9 Mathematics and appears in school tests and the end-of-year exam.

Step-by-step method

  1. Find the right angle in the triangle.
  2. The side opposite it is the hypotenuse.
  3. Add the squares of the other two sides to find the hypotenuse, or subtract to find a shorter side.

Common mistake

Treating one of the shorter sides as the hypotenuse, which gives an impossible answer.

Related geometry terms

Frequently asked questions

What does hypotenuse mean in Grade 9 Maths?

The hypotenuse is the side opposite the right angle in a right-angled triangle. It is always the longest side, and in the Theorem of Pythagoras it is the c in c² = a² + b².

When do you learn about hypotenuse?

Hypotenuse is taught in the geometry section of CAPS Grade 9 Mathematics and is used again in Grades 10 to 12.

How do I practise questions involving hypotenuse?

Snap a question that uses hypotenuse into Snap&Learn with your grade set to Grade 9, or work through the Grade 9 topic guide and practice papers.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.