I want to find how far back I should move to take a 35mm equivalent photo on a 1.6x crop sensor camera. Effective focal lengths are multiplied by 1.6x when using this crop sensor, so a photo shot at 20mm is instead 32mm, 50mm is 80mm, etc. To try and figure this out, I've made a diagram of two triangles:
The two triangles have the same base width but have varying heights. The topmost angle of the green triangle is $25°$ and the black triangle is $40°$. I've chosen these arbitrarily, the only important bit is the black triangle's angle is $1.6$ times the green one. $40 = 25 * 1.6$.
To help illustrate, I've drawn a red box between the two triangle bases, representing the distance needed to achieve the same focal length.
What is the height of the red box, or rather the difference between heights of the two triangles?