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The word 三角 is often used in judo to describe a position enclosing your opponent's head and arm in a "triangle" created by interlocking your legs. However this word is occasionally spelled sangaku (as opposed to the expected sankaku):
37. Omote-sangaku
38. Ashi-sangaku-garami
...
45. Yoko-sangaku
- Fighting Judo, Katsuhiko Kashiwazaki
Is this just a typo, or an example of rendaku in the author's dialect?
i.e. is 三角 ever pronounced さんがく?
Weblio's hits for さんがく don't include 三角, which would suggest that this isn't standard.
Google searches for "よこさんがく" and "あしさんがく" also return zero hits, while searches for "よこさんかく" and "あしさんかく" with the unvoiced か return relevant sites.
I see that Kashiwazaki is from Iwate, and I believe that this kind of softening or additional voicing is a feature of dialects in the northeast. I lived in Morioka for a while years ago, and was interested to hear such additional voicing among the speakers there, things like 度【たび】 being pronounced as たんび, or a kind of interjectionary particle a bit like ね or そう, but realized as んだ.
→ This leads me to think that the さんがく pronunciation might be an expression of Kashiwazaki's Iwate-ben.
Short answer to you question would be neither of them is "right". Only right way to write that word in English is "triangle" (assuming the translation was correct).
Long Answer: Japanese is ONLY written with Kanjis, Hiragana and Katakana characters (plus few more obscure character sets). Japanese is NOT written in latin characters. Any Japanese written with latin chracters is just phonetics, what the Japanese word sounds similar to some other language (like English). Japanese written in latin is a learning aid, not real language. There is no one right way to spell Japanese words with latin characters. Debating latin spelling of Japanese words is like debating correct spelling for the sound a wind makes. Only right way to spell Japanese words is in Japanese.
In Japan event the signs for train station and cities have varying spelling in latin character. For a bad example there is only one right way to write name of Japan's capital is 東京. Well, if you want to nit pick there are like 4 different character sets you can use but none of them is latin. So 東京 written in latin characers the "Tohkyo", "Tokio", "Tokyo", "Tookio" all equally right or wrong. Note that in this case a English translation of the capital's name is "Tokyo", like the "triangle" would be for the word in the question.
