To find the hypotenuse of a right triangle, use the Pythagorean theorem formula:
c=a2+b2c=\sqrt{a^2+b^2}c=a2+b2
where ccc is the hypotenuse (the longest side opposite the right angle), and aaa and bbb are the lengths of the other two sides (legs) of the triangle.
How to find the hypotenuse:
- Square the lengths of both legs aaa and bbb.
- Add the squares together.
- Take the square root of the sum to get ccc, the hypotenuse.
This method works only for right triangles.
Additional ways:
- If you know an angle (other than the right angle) and the length of one leg, you can use trigonometric functions like sine to find the hypotenuse:
c=asin(α)c=\frac{a}{\sin(\alpha)}c=sin(α)a
where α\alpha α is the known angle and aaa is the side opposite that angle.
- If you know the area of the triangle and one leg, you can find the hypotenuse using area formulas and the Pythagorean theorem.
The hypotenuse is always the longest side in a right triangle.
