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To solve for the missing side of this right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle:

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

Where:
- \( a \) and \( b \) are the legs of the triangle (the two shorter sides),
- \( c \) is the hypotenuse (the longest side, opposite the right angle).

In this image:
- One leg is \( 5.2 \, \text{mm} \),
- The hypotenuse is \( 7 \, \text{mm} \),
- We need to find the length of the other leg.

Let the unknown leg be \( x \). Applying the Pythagorean theorem:

\[
5.2^2 + x^2 = 7^2
\]

First, square the known values:

\[
5.2^2 = 27.04 \quad \text{and} \quad 7^2 = 49
\]

Now substitute these into the equation:

\[
27.04 + x^2 = 49
\]

Solve for \( x^2 \):

\[
x^2 = 49 - 27.04 = 21.96
\]

Now, take the square root of both sides:

\[
x = \sqrt{21.96} \approx 4.69
\]

So, the length of the missing side is approximately \( 4.7 \, \text{mm} \) (rounded to the nearest tenth of a millimeter).

Would you like further details on the steps, or do you have any other questions?

Here are 5 related questions to expand on this:

1. How do you determine which side of a triangle is the hypotenuse?
2. What are some other real-life applications of the Pythagorean theorem?
3. How can you apply the Pythagorean theorem to 3D shapes?
4. How would you solve for a missing angle in a right triangle using trigonometry?
5. What happens if the triangle has no right angle—can we still use the Pythagorean theorem?

**Tip:** When dealing with triangles, it's important to identify right angles, as they determine whether the Pythagorean theorem applies.

Find the missing side length to the nearest tenth of a millimeter. Given a right triangle with one leg measuring 5.2 mm and the hypotenuse measuring 7 mm.

Learn how to find the missing side of a right triangle using the Pythagorean Theorem. In this example, a triangle has one leg measuring 5.2 mm and the hypotenuse measuring 7 mm. Detailed step-by-step calculations show how to solve for the missing side length to the nearest tenth of a millimeter. Suitable for students in Grades 7-9.

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