Question

what is the value of h in the figure below?

Answer 1

It is useful to note how all three triangles (the main one and each smaller one inside) are all similar triangles to each other.

Some of the angles can be figured simply because we have triangles and right angles -- the other angles tend to 'fall' into place because they have to add up to 90 degrees.
The most useful pair of similar triangles here is the set of each smaller one. You can relate the sides between the right angle and each acute angle using side ratios. This equates our h to known values.