Triangle Height Help

I need to find the height of h.

To solve that equation, you need to know about the proportional ratios in triangles. When you have a right triangle like that, and draw the line h from the right angle to be perpendicular to the hypotenuse, the triange is split in two (obviously). These two triangles are similar figures to each other, as well as the largest triangle. So, the ratios on each are the same.

h / 5*root7 = 10 / 15

Approach this in an orderly manner. When you're stuck with problems like this, it helps if you trace each triangle so that they are separate and corresponding sides are in the same position.
I will call the triangles, in order of size, Triangle A, B, and C.
The hypotenuse of Triangle C is 2/3 that of Triangle A's.
With that scale in mind, we can conclude that
(2/3)5*root7 =height
You don't need the Pythagorean Theorem for this, just reasoning and ratios.
Is that helpful? (My math teacher will be so proud of me.)

What they said, man. I fall asleep in that class. (My teacher sucks)