Explanation

A right triangle is a triangle that has one angle equal to \(90^\circ\).

In a right triangle, there is a special relationship between the three sides called the Pythagorean formula.

This formula allows us to find a missing side when we know the other two sides.

The Pythagorean formula can be used only with right triangles.

Formula / Rule

In any right triangle:

\(c^2 = a^2 + b^2\)

Where:

◉ \(c\) is the hypotenuse—the longest side, opposite the \(90^\circ\) angle.

◉ \(a\) and \(b\) are the other two sides, called the legs.

To find the hypotenuse, add the squares of the two legs.
To find a missing leg, subtract the square of the known leg from the square of the hypotenuse.
The hypotenuse must always be used as \(c\).

Find the hypotenuse \(x\) when the other two sides are \(3\) and \(4\).

Step 1: Substitute the known values.

\(x^2 = 3^2 + 4^2\)

Step 2: Calculate the squares.

\(x^2 = 9 + 16\)

\(x^2 = 25\)

Step 3: Take the square root of both sides.

\(x = \sqrt{25}\)

\(x = 5\)

✅ So, the hypotenuse is \(5\).