Wow. 1975 was a most craptacular year for new car models. AMC Pacer, Chevy Monza, Ford Grenada, Chrysler Cordoba; the mid-1970s were a particularly bad time for cars. Fresh off an oil crisis (with another looming) and facing draconian environmental regulations, the companies that only a few years prior had brought us the Chevelle, Boss Mustang, and Charger were now attempting, poorly, to bring us "compact" cars.
Fortunately, British manufacturers had been making more with less for many years. 1975 saw the introduction of the Triumph TR-7, replacing the more traditionally-styled TR6. The TR7 weighed the same as the TR6, yet was powered by an inline 4-cylinder engine rather than the 6-cylinder from the TR6. This would be addressed by the 3.5L V8 dropped into the TR8, which was styled very similarly to the TR7.
At a time when American cars were bogged down by emissions control and using much smaller engines than only a few years prior (consider the Chevy Monza's 2.3L I4 with 78 HP with the 454 V8 in the '70 Chevelle...), offering a small, light, nimble British sports car with a significant racing heritage made a lot of sense. There wasn't much on this side of the pond to give the TR7 much of a race, and for exotic, "wow" factor the "wedge" shape was certainly different.
And that convertible version? Oh my...
That is all.