a² + b² = c²
First find out the length of the line in the middle. We know that a² + 16² = 27², which means a = √473
Now write out all the equations for all the right triangles in the diagram.
Let the side of the base of the triangle be x and the remaining sides of z be y.
x² + 27² = (16+ y)²
y² + (√473)² = x²
From here solve and find y. Once you get y, y + 16 is your z, the answer.
