/sci/ - Science & Math

I need help on this exercise from Humphreys' reflection groups. Note that [math]\Delta[/math] is a simple system and the root system [math] \Phi [/math] is not necessarily crystallographic. [math]\mathrm{ht}(\beta)[/math] is defined as [math]\sum_{i=1}^nc_i[/math] if [math]\beta = \sum_{i=1}^nc_i\alpha_i[/math] where [math]\alpha_i \in \Delta[/math] I tried approaches using the scalar product but nothing worked and now I don't even know where to start.