Question

Pythagorean Theorem
FIND SLANT HEIGHT
a = 12
b =1 0
c= ?
ztep by step

Answer 1

To find the slant height \( c \) using the Pythagorean theorem, you can use the formula:

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

where \( a \) and \( b \) are the two perpendicular sides of a right triangle, and \( c \) is the hypotenuse (slant height in this case).

Given:
- \( a = 12 \)
- \( b = 10 \)

Let's calculate \( c \) step by step:

### Step 1: Square the values of \( a \) and \( b \)

\[
a^2 = 12^2 = 144
\]

\[
b^2 = 10^2 = 100
\]

### Step 2: Add the squares of \( a \) and \( b \)

\[
a^2 + b^2 = 144 + 100 = 244
\]

### Step 3: Take the square root of the sum

\[
c = \sqrt{244}
\]

### Step 4: Simplify the square root if necessary

\[
\sqrt{244} = \sqrt{4 \times 61} = 2\sqrt{61}
\]

Using a calculator to approximate:

\[
\sqrt{244} \approx 15.62
\]

### Conclusion
The slant height \( c \) is approximately \( 15.62 \) units, or expressed exactly, \( 2\sqrt{61} \).