Final answer:
To find the height the ladder will reach, use the Pythagorean theorem.
Step-by-step explanation:
To find the height the ladder will reach, we can use the Pythagorean theorem. The ladder, the wall, and the distance from the wall form a right triangle. The base of the triangle is 12 feet, the ladder is the hypotenuse, and the height of the triangle is what we need to find. Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Where a = 12 feet (the base), b = height, and c = 35 feet (the ladder).
Plugging in the values, we have:
12^2 + b^2 = 35^2
Simplifying, we get:
144 + b^2 = 1225
Subtracting 144 from both sides:
b^2 = 1225 - 144
b^2 = 1081
Taking the square root of both sides:
b = sqrt(1081)
Rounding to the nearest tenth, the ladder will reach approximately 32.9 feet high.