Question

FIND SLANT HEIGHT
a = 12
b =5
c= ?
ztep by step

Answer 1

To find the slant height (c) of a right triangle formed by the height (a) and the base (b), you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle:

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

Where:
- \(c\) is the hypotenuse (the slant height, in this case),
- \(a\) is the height,
- \(b\) is the base.

Given:
- \(a = 12\)
- \(b = 5\)

### Step 1: Square both sides
Calculate \(a^2\) and \(b^2\):

\[
a^2 = 12^2 = 144
\]
\[
b^2 = 5^2 = 25
\]

### Step 2: Add \(a^2\) and \(b^2\)
Now add the two results:

\[
a^2 + b^2 = 144 + 25 = 169
\]

### Step 3: Take the square root
Now, to find \(c\):

\[
c^2 = 169
\]

Taking the square root of both sides gives:

\[
c = \sqrt{169} = 13
\]

### Conclusion
The slant height \(c\) is **13**.