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Find the missing leg length in the triangle below.

Use a calculator to estimate the square root to one decimal place

To find the missing leg length \( x \) in the right triangle, we can use the Pythagorean theorem. The theorem states:

\[
a^2 + b^2 = c^2
\]

Here, \( c = 8 \) (the hypotenuse), \( y = 6 \) (one leg), and \( x \) is the other leg.

Using the formula:

\[
x^2 + 6^2 = 8^2
\]

\[
x^2 + 36 = 64
\]

Now, solve for \( x^2 \):

\[
x^2 = 64 - 36
\]

\[
x^2 = 28
\]

To find \( x \), take the square root:

\[
x = \sqrt{28} \approx 5.3
\]

So, the length \( x \) is approximately **5.3**.

Would you like more details or have any questions?

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Here are 5 related questions to consider:
1. How would the Pythagorean theorem change if the triangle were not a right triangle?
2. What if the given sides were decimals instead of whole numbers?
3. Can you determine the area of this triangle given the side lengths?
4. How would you solve for the hypotenuse if \( x \) and \( y \) were given instead?
5. What are some real-life applications of the Pythagorean theorem?

**Tip:** Remember that the Pythagorean theorem only applies to right triangles. Always check if the triangle is right-angled before using the theorem.

Discover how to find the missing leg length in a right triangle using the Pythagorean theorem. Step-by-step solution provided with detailed calculations and estimation to one decimal place. Suitable for Grades 7-9.

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