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Calculate the length of the unknown side for the triangle shown.

To calculate the length of the unknown side for the given right triangle, we can use the **Pythagorean theorem**. The formula is:

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

Where:
- \( c \) is the hypotenuse (260 mm in this case),
- \( a \) is one of the legs (120 mm in this case),
- \( b \) is the unknown side (which we are looking to solve for).

Let's plug in the values and solve for \( b \).

\[
260^2 = 120^2 + b^2
\]

Now, I'll calculate the value of \( b \).It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, you can calculate the unknown side yourself using the following steps:

1. Square the hypotenuse and the given leg:
   \[
   260^2 = 67600 \quad \text{and} \quad 120^2 = 14400
   \]

2. Subtract the square of the leg from the square of the hypotenuse:
   \[
   67600 - 14400 = 53200
   \]

3. Take the square root of the result:
   \[
   \sqrt{53200} \approx 230.7 \, \text{mm}
   \]

So, the length of the unknown side \( b \) is approximately **230.7 mm**.

Let me know if you have any questions, or if you'd like further clarification.

Here are 5 related questions for practice:
1. How would you use trigonometry to find angle \( \theta \) in this triangle?
2. Can the Pythagorean theorem be used for any type of triangle?
3. How would you calculate the area of this right triangle?
4. What would be the perimeter of this triangle?
5. If the hypotenuse was doubled, how would that affect the length of the other sides?

**Tip:** For right triangles, trigonometric functions like sine, cosine, and tangent can be useful when you know one angle and need to find unknown sides.

Learn how to calculate the length of the unknown side of a right triangle with one leg measuring 120 mm and a hypotenuse of 260 mm using the Pythagorean Theorem. Follow a step-by-step guide, perfect for students in Grades 8-10.

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