Skill: Apply the Pythagorean theorem

In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side. The other two sides are called the legs.

Use the Pythagorean theorem:

$$a^2+b^2=c^2$$

where $a$ and $b$ are the legs and $c$ is the hypotenuse.

Example: A right triangle has a hypotenuse of $13$ cm and one leg of $5$ cm. Find the length of the other leg.

1. Let the unknown leg be $x$. Substitute the known lengths into the formula:

$$5^2+x^2=13^2$$

2. Evaluate the squares:

$$25+x^2=169$$

3. Subtract $25$ from both sides:

$$x^2=144$$

4. Take the square root of both sides:

$$x=\sqrt{144}=12$$

The unknown leg is $12$ cm. Check: $5^2+12^2=25+144=169=13^2$, so the answer is correct.