Answer & Step-by-step explanation:
This is a classic right triangle problem.
The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the wall is one leg of the triangle, and the distance from the base of the ladder to the wall is the other leg.
According to the problem, the ladder is 12 feet long and is leaning 10 feet up the wall. Therefore, we can use the Pythagorean theorem to find the distance from the base of the ladder to the wall:
c^2 = a^2 + b^2
where c is the length of the ladder (12 feet), a is the distance from the ladder's base to the wall (what we need to find), and b is the height the ladder is up the wall (10 feet).
Plugging in the values we have:
12^2 = a^2 + 10^2
Simplifying:
144 = a^2 + 100
Subtracting 100 from each side:
44 = a^2
Taking the square root of both sides:
a ≈ 6.63
Therefore, the distance from the base of the ladder to the wall is approximately 6.63 feet.