Question

Pythagorean Theorem
a = 11
B ?
c = 15
step by step

Answer 1

To find the length of side \( B \) in a right triangle using the Pythagorean Theorem, we'll use the formula:

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

Where:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg (which we'll denote as \( B \) here),
- \( c \) is the hypotenuse.

Given:
- \( a = 11 \)
- \( c = 15 \)
- We need to find \( B \) (or \( b \)).

### Step 1: Substitute the known values into the equation.
\[
11^2 + B^2 = 15^2
\]

### Step 2: Calculate \( 11^2 \) and \( 15^2 \).
\[
121 + B^2 = 225
\]

### Step 3: Solve for \( B^2 \).
Subtract 121 from both sides:
\[
B^2 = 225 - 121
\]
\[
B^2 = 104
\]

### Step 4: Take the square root of both sides to find \( B \).
\[
B = \sqrt{104}
\]

### Step 5: Simplify \( \sqrt{104} \).
\[
\sqrt{104} = \sqrt{4 \times 26} = \sqrt{4} \times \sqrt{26} = 2\sqrt{26}
\]

### Final Answer:
The length of side \( B \) is:
\[
B = 2\sqrt{26} \approx 10.20
\]
Thus, \( B \) is approximately 10.20 units.