Three standard routes

If both legs are known, use c=sqrta2+b2c=sqrt{a^2+b^2}. If an acute angle is known, use cosine or sine depending on whether the given side is adjacent or opposite.

The hypotenuse is always opposite the right angle and is always the longest side.

Good uses

  • Checking triangle work before drawing or measurement tasks.
  • Switching between Pythagorean and trigonometric setups.
  • Teaching why a right triangle can be solved from different data pairs.