What is the value of x in the diagram below?

You have a big right triangle and a small right triangle.
The point where x meets 20 is an acute angle in both triangles.
Cosine of an angle in a right triangle is (adjacent side)/(hypotenuse).
Cosine of that angle in the big triangle is x/56.
Cosine of that angle in the small triangle is 20/x.
But it's the same angle, so x/56 = 20/x.
Cross-multiply: x^2 = 1120 = 16•70.
X = √(16•70) = 4√70 .