data structures - Calculating the height of a binary tree -

i need theory on calculating height of binary tree, typically notation.

i have read following article:

calculating height of binary tree

and 1 of posts gives following notation:

height(node) = max(height(node.l), height(node.r)) + 1

let's assume have following binary tree:

     10    /   \     5    30  / \   /  \  4  8  28  42 

do therefore calculate max value on left node (8) , max node on right (42) , add 1? don't quite understand how notation works in order calculate height of tree.

i'll try explain how recursive algorithm works:

height(10) = max(height(5), height(30)) + 1  height(30) = max(height(28), height(42)) + 1 height(42) = 1 (no children) height(28) = 1 (no children)  height(5) =  max(height(4), height(8)) + 1 height(4) = 1 (no children) height(8) = 1 (no children) 

so if want calculate height(10), have expand recursion down, , substitute results backwards.

height(5)  = max(1, 1) + 1 height(30) = max(1, 1) + 1 height(10) = max(2, 2) + 1 height(10) = 3