Line KC is perpendicular to the square ABSD, KA = √ 34, AC = 3√ 2. Find KB.

1. By the condition of the problem, it is known that the straight line KС is perpendicular to the plane of the square of the AВСD, while KA = √34, AC = 3 √2.

2. In the calculations, we will use the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs:

Let’s define the length of the CК as a leg in a right-angled triangle AKC

КС² = KA² – AC² or КС = √34² – (3 √2) ² = √34 – 9 * 2 = √34 – 18 = √16 = 4.

3. Calculate the side of the square 2 * BC² = (3 √2) ², whence BC = √9 = 3.

4. Let’s calculate the value of KВ = √KC² + BC² = √4² + 3² = √16 + 9 = √25 = 5.

Answer: Looking for CВ = 5.