Question

Show me the steps for finding the length of hypotenuse

Answer 1

To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The formula is:

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

Here are the steps to find the length of the hypotenuse:

### Step 1: Identify the lengths of the two legs
Determine the lengths of the two sides of the triangle that form the right angle. Let's denote these lengths as \(a\) and \(b\).

### Step 2: Square the lengths of the legs
Calculate the square of each of the two lengths:
- \(a^2\)
- \(b^2\)

### Step 3: Add the squares
Add the results from step 2 together:
\[ a^2 + b^2 \]

### Step 4: Take the square root
To find the length of the hypotenuse (c), take the square root of the sum obtained in step 3:
\[ c = \sqrt{a^2 + b^2} \]

### Example
Let's say the lengths of the legs are:
- \(a = 3\)
- \(b = 4\)

1. Square the lengths:
- \(3^2 = 9\)
- \(4^2 = 16\)

2. Add the squares:
\[ 9 + 16 = 25 \]

3. Take the square root:
\[ c = \sqrt{25} = 5 \]

So, the length of the hypotenuse is \(5\).