Mastering the Pythagorean Theorem for CAASPP Math Success

If a right triangle has legs measuring 6 cm and 8 cm, what is the length of the hypotenuse?

• A. 10 cm
• B. 12 cm
• C. 14 cm
• D. 15 cm

Answer: (A)

To determine the length of the hypotenuse in a right triangle when the lengths of the legs are known, we can utilize the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, it can be expressed as: c² = a² + b². In this case, the lengths of the legs are 6 cm and 8 cm. By applying the theorem: 1. Calculate the squares of the legs: - 6 cm squared is 36 (6² = 36). - 8 cm squared is 64 (8² = 64). 2. Add the squares of the legs together: - 36 + 64 equals 100. 3. To find the hypotenuse, take the square root of the sum: - The square root of 100 is 10 cm (√100 = 10). Thus, the length of the hypotenuse in this right triangle is correctly calculated to be 10 cm. This demonstrates a solid application of the Pythagorean theorem,

Alright, math enthusiasts! Let’s tackle something that often perplexes students prepping for the California Assessment of Student Performance and Progress (CAASPP) Math exams: the Pythagorean theorem. If you’ve ever had to find the length of a hypotenuse in a right triangle, you’re in the right spot. You know what? Understanding this theorem will not only help you ace your math exam but could impress your friends during a friendly game of trivia!

So, What’s the Big Deal About the Pythagorean Theorem?

Here’s the lowdown: the Pythagorean theorem is a fundamental principle in geometry. It connects the lengths of the sides of a right triangle, which is a triangle that has one 90-degree angle. This theorem tells us that if you take the square of the length of the hypotenuse (that’s the longest side opposite the right angle), it’s equal to the sum of the squares of the lengths of the other two sides. The formula goes like this:

[ c² = a² + b² ]

Where:

• ( c ) is the length of the hypotenuse,

• ( a ) and ( b ) are the lengths of the legs.

Breaking It Down: An Example

Let’s help you visualize how this plays out. Suppose you have a right triangle with legs measuring 6 cm and 8 cm. The question is, what’s the length of the hypotenuse?

1. Square the legs:

• So, ( 6² ) (that’s 6 times 6) is 36.

• And ( 8² ) is 64.

2. Add those squares together:

• 36 + 64 equals 100.

3. Now, here comes the fun part—finding the hypotenuse! You take the square root of 100. What's that? It’s 10! So, the hypotenuse is 10 cm long!

Pretty straightforward, right? Throughout your studies, you’ll find that this theorem opens the door to solving many problems related to right triangles—not just in exams but in real-life situations! Think about it. If you were constructing a ramp for a skateboarder, understanding angles and lengths would be crucial.

Why Should You Care?

Not only does grasping the Pythagorean theorem bolster your exam performance, but it also lays the groundwork for more advanced topics in math. Geometry isn’t just about solving problems; it provides tools you’ll use in fields like engineering, architecture, and even computer science.

And if you find yourself scratching your head while studying, remember that practice is key. Working with various problems will strengthen your understanding and confidence!

Wrap It Up!

To sum it up, knowing how to apply the Pythagorean theorem will be a game changer for your CAASPP preparation. So next time you find a right triangle—be it in your notes or out in the world—don’t shy away. Grab your pencil, apply the theorem, and confidently find that hypotenuse! You’ve got this!