https://file.aiquickdraw.com/mathbot/file/1729998564883efowk5z6.jpg

From the image, the problem asks for the length of the unknown side of a right triangle where the two other sides are given as 4 mm and 4.3 mm. To solve this, we can use the **Pythagorean theorem**, which is expressed as:

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

Where:
- \( a \) and \( b \) are the legs of the triangle,
- \( c \) is the hypotenuse.

We need to determine which side is the hypotenuse, and from the diagram, it appears that 4.3 mm is the hypotenuse because it is the longest side. So, we set up the equation:

\[
4^2 + x^2 = 4.3^2
\]

Now, solve for \( x \), which is the unknown side:

1. \( 4^2 = 16 \)
2. \( 4.3^2 = 18.49 \)
3. Substitute into the equation:

\[
16 + x^2 = 18.49
\]

4. Subtract 16 from both sides:

\[
x^2 = 18.49 - 16 = 2.49
\]

5. Take the square root of both sides:

\[
x = \sqrt{2.49} \approx 1.58 \text{ mm}
\]

Thus, the exact length of the unknown side is \( \sqrt{2.49} \) mm, and the approximate length is **1.58 mm**.

Would you like more details or have any questions? 

Here are 5 related questions you can explore:
1. How do you determine which side is the hypotenuse in a right triangle?
2. How does the Pythagorean theorem apply to triangles in 3D space?
3. What happens if one of the triangle's side lengths is irrational?
4. How can the Pythagorean theorem be used in coordinate geometry?
5. Can the Pythagorean theorem be used in non-right triangles?

**Tip**: When solving problems involving radicals, always simplify your final answer if possible.

Find the length of the unknown side of each triangle. Give the exact length and an approximate length.

Learn to find the unknown side length of a right triangle with given sides of 4 mm and 4.3 mm. This solution applies the Pythagorean theorem, providing an exact and approximate answer. Ideal for Grades 7-9 students.

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