"the height of which" is correct and can be used in written English.
It is commonly used to refer to the height of something that has already been mentioned or is being compared to something else. Example: The tree, the height of which reached over 50 feet, provided cooling shade on hot summer days.
The female initiates vertical circular turnovers, at the height of which she extrudes a few eggs.
In the mercury barometer, atmospheric pressure balances a column of mercury, the height of which can be precisely measured.
The design, however, has remained unchanged, with the exception of the pedestal base, the height of which was increased in 1945.
Donald Trump wants a solid wall, the height of which must be no less than 7ft, erected between him and the other candidates during the debate.
Growth of islands as ridges was observed, the height of which was as high as 200 nm.
The sexual cycle in males, the height of which in some forms is referred to as the rut, is, not surprisingly, usually correlated with that of the females.
But, in the view of many contemporaries, and perhaps his own, he never quite achieved the heights of which he was capable.
Just as in life, mutual strength lifts each of us, so we can soar to the heights of which we're all capable … So, sisters, grab your pompoms and start cheering for someone else's future – you may be surprised at the actions it inspires in you".
Neither player consistently reached the heights of which they are capable, and Higgins - chasing a third title in five years, and fourth overall - capitalised on several errors with runs of 63, 65 and 73 to move within one frame of victory.
The magnitudes of the vector elements can be plotted as series of peaks, the heights of which indicate the relative contribution of each band to the successive separations between groups.
Figure 6 shows the scheme of the RC column, the clear height of which is 2750 mm.
