Sure! Let's walk through the application of the Pythagorean theorem step-by-step, using the values given.
### Step 1: Identify the lengths of the legs
We are given:
- One leg [tex]\(a\)[/tex] of the triangle is 3 units.
- The other leg [tex]\(b\)[/tex] of the triangle is 4 units.
### Step 2: Calculate the squares of each leg
First, we calculate the square of leg [tex]\(a\)[/tex]:
[tex]\[ a^2 = 3^2 = 9 \][/tex]
Next, we calculate the square of leg [tex]\(b\)[/tex]:
[tex]\[ b^2 = 4^2 = 16 \][/tex]
### Step 3: Sum the squares of the legs
Now, we sum the squares of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[ a^2 + b^2 = 9 + 16 = 25 \][/tex]
### Step 4: Calculate the square root to find the hypotenuse
Finally, to find the length of the hypotenuse [tex]\(c\)[/tex], we take the square root of the sum:
[tex]\[ c = \sqrt{25} = 5.0 \][/tex]
### Summary of the results
- [tex]\(a^2 = 9\)[/tex]
- [tex]\(b^2 = 16\)[/tex]
- [tex]\(a^2 + b^2 = 25\)[/tex]
- [tex]\(c = 5.0\)[/tex]
Thus, for a right triangle with legs [tex]\(a = 3\)[/tex] and [tex]\(b = 4\)[/tex], the hypotenuse [tex]\(c\)[/tex] is 5.0 units.
