To find the height at which the ladder meets the wall, we can use the Pythagorean theorem. The ladder acts as the hypotenuse of a right triangle, with the distance from the wall to the base of the ladder as one leg and the height at which the ladder meets the wall as the other leg.
Let:
- \( a \) be the height at which the ladder meets the wall (the vertical leg).
- \( b \) be the distance from the wall to the base of the ladder (the horizontal leg), which is 5 m.
- \( c \) be the length of the ladder (the hypotenuse), which is 13 m.
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Substituting the known values:
\[ a^2 + 5^2 = 13^2 \] \[ a^2 + 25 = 169 \] \[ a^2 = 169 - 25 \] \[ a^2 = 144 \]
Now, taking the square root of both sides:
\[ a = \sqrt{144} = 12 \]
Thus, the height above the ground where the ladder meets the wall is 12 m.
The correct answer is:
C. 12 m