If a right triangle has one leg that measures 12 in and the hypotenuse measures 36 in, what is the length of the other leg?

 

To find the length of the other leg in a right triangle, we can use the **Pythagorean theorem**, which is:

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

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

Given:
- One leg \(a = 12\) in,
- The hypotenuse \(c = 36\) in.

We need to find the other leg \(b\).

Using the formula, we can solve for \(b\):

\[
12^2 + b^2 = 36^2
\]

\[
144 + b^2 = 1296
\]

\[
b^2 = 1296 - 144
\]

\[
b^2 = 1152
\]

Taking the square root of both sides:

\[
b = \sqrt{1152} \approx 33.94 \text{ in}
\]

So, the length of the other leg is approximately **33.94 inches**.

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

Here are 5 related questions to explore further:
1. How would the length of the other leg change if the hypotenuse was shorter?
2. Can you apply the Pythagorean theorem to a triangle that is not a right triangle?
3. What is the perimeter of this triangle?
4. How would you find the area of the right triangle given these dimensions?
5. Can you find the angles of this triangle using trigonometry?

**Tip:** The Pythagorean theorem only applies to right triangles, so always confirm the triangle type before using it!

If a right triangle has one leg that measures 12 in and the hypotenuse measures 36 in, what is the length of the other leg?

Learn how to find the length of the other leg in a right triangle where one leg is 12 inches and the hypotenuse is 36 inches. This detailed step-by-step solution uses the Pythagorean theorem and is suitable for students in Grades 8-10.

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