In right triangles, the Pythagorean theorem is your best friend! It states that $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse (the side opposite the right angle). When you're trying to find a missing leg, you'll be given the length of the hypotenuse and one leg. Just plug those values into the formula and solve for the unknown leg!
For example, if you know the hypotenuse is 5 and one leg is 3, you can find the other leg like this: $3^2 + b^2 = 5^2$, which simplifies to $9 + b^2 = 25$. Subtracting 9 from both sides gives $b^2 = 16$. Taking the square root of both sides, we find that $b = 4$. So, the missing leg is 4!
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Hypotenuse | A. The side opposite the right angle in a right triangle |
| 2. Leg | B. Either of the two shorter sides in a right triangle |
| 3. Right Angle | C. An angle that measures exactly 90 degrees |
| 4. Pythagorean Theorem | D. $a^2 + b^2 = c^2$ |
| 5. Square Root | E. A value that, when multiplied by itself, gives the original number |
Use the following words to fill in the blanks: hypotenuse, legs, Pythagorean, right, square root.
In a ______ triangle, the longest side is called the __________. The other two sides are called __________. The __________ Theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse. To find a missing leg, you often need to calculate the __________.
Can the length of a leg in a right triangle ever be longer than the hypotenuse? Explain why or why not.
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