https://file.aiquickdraw.com/mathbot/file/17305694264011fawgerl.jpg

To solve this problem, we can use the **Pythagorean theorem**, which states that in a right triangle, the square of the hypotenuse (\( c \)) is equal to the sum of the squares of the other two legs (\( a \) and \( b \)):

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

In this triangle:
- The hypotenuse is the longest side, which is given as \( 7 \, \text{cm} \).
- One leg is given as \( 2 \, \text{cm} \).
- The other leg, \( b \), is the unknown we need to find.

### Step-by-Step Solution

1. **Set up the equation using the Pythagorean theorem**:
   \[
   7^2 = 2^2 + b^2
   \]

2. **Substitute the values and simplify**:
   \[
   49 = 4 + b^2
   \]

3. **Isolate \( b^2 \)** by subtracting 4 from both sides:
   \[
   b^2 = 49 - 4
   \]
   \[
   b^2 = 45
   \]

4. **Solve for \( b \)** by taking the square root of both sides:
   \[
   b = \sqrt{45}
   \]
   \[
   b \approx 6.7
   \]

### Final Answer
The length of the missing leg \( b \) is approximately **6.7 cm**, rounded to the nearest tenth.

Would you like more details, or do you have any questions?

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Here are five related questions to expand on this topic:
1. How would the answer change if the given leg was 3 cm instead of 2 cm?
2. Can you calculate the area of this triangle with the given and found side lengths?
3. How does the Pythagorean theorem apply to non-right triangles?
4. What is the relationship between the sides in a 45°-45°-90° triangle?
5. How can we use trigonometry to solve for unknown sides in a right triangle?

**Tip:** Remember, the Pythagorean theorem only applies to right triangles.

What is the length of the missing leg? If necessary, round to the nearest tenth. Given: hypotenuse = 7 cm, one leg = 2 cm.

Learn how to find the length of the missing leg in a right triangle with a hypotenuse of 7 cm and a known leg of 2 cm. This solution applies the Pythagorean theorem, making it suitable for Grade 8 students.

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