Apply the Pythagorean theorem

The Pythagorean theorem relates the side lengths of a right triangle: for legs $a$ and $b$ and hypotenuse $c$ , the side opposite the right angle, $a^2+b^2=c^2$ . Applying this relationship involves identifying the hypotenuse, finding an unknown side length using squares and square roots, and interpreting exact or approximate measurements in geometric and coordinate contexts; it does not extend here to non-right triangles or trigonometric generalizations.

Detailed Explanation: 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.

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

5^2+x^2=13^2

Evaluate the squares:

25+x^2=169

Subtract $25$ from both sides:

x^2=144

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.

Learn by doing: Apply the Pythagorean theorem

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Pythagorean Theorem - Either Missing Length - Labelled Sides (Radical)

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Apply the Pythagorean theorem

Detailed Explanation: Apply the Pythagorean theorem

Learn by doing: Apply the Pythagorean theorem

Practice with unlimited practice problems

Practice:

Pythagorean Theorem - Either Missing Length - Labelled Sides (Radical)