https://file.aiquickdraw.com/mathbot/file/17255897875267exzzl41.jpg

This image shows a right triangle where the lengths of the hypotenuse and one leg are given, and we are asked to find the length of the unknown side. Here's the information we have:

- Hypotenuse: 12.1 m
- One leg: 3.6 m
- The unknown side is represented by a question mark.

We can apply **Pythagoras' Theorem** to solve for the unknown side. Pythagoras' Theorem states:

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

Where:
- \( c \) is the hypotenuse (12.1 m),
- \( a \) is one leg (3.6 m),
- \( b \) is the unknown side.

We can rearrange the equation to solve for the unknown side \( b \):

\[
b = \sqrt{c^2 - a^2}
\]

Let's calculate that now.The length of the unknown side is approximately **11.6 meters** when rounded to three significant figures.

Do you have any questions or would you like further details on this calculation?

Here are 5 related questions to expand on the topic:
1. How does Pythagoras' theorem work for non-right triangles?
2. Can you apply the Pythagorean theorem to find the hypotenuse if both legs are given?
3. What is the significance of the unit of measurement in geometry problems?
4. How do you calculate the area of a right triangle using the given side lengths?
5. What is the relation between trigonometric ratios and right triangles?

**Tip:** Always ensure the triangle is a right triangle before applying Pythagoras' theorem, as it only applies to those specific cases.

For the triangle pictured above, calculate the value of the unknown side.

Learn how to use the Pythagorean Theorem to solve for the missing side of a right triangle when given the hypotenuse and one leg. This problem involves the formula c^2 = a^2 + b^2 and is suitable for students in Grades 7-9.

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