Answer by taking a quote from the following article:

Sir Richard Francis Burton  (; 19 March 1821 - 20 October 1890) was a British explorer, geographer, translator, writer, soldier, orientalist, cartographer, ethnologist, spy, linguist, poet, fencer, and diplomat. He was famed for his travels and explorations in Asia, Africa and the Americas, as well as his extraordinary knowledge of languages and cultures. According to one count, he spoke 29 European, Asian and African languages.

Burton died in Trieste early on the morning of 20 October 1890 of a heart attack. His wife Isabel persuaded a priest to perform the last rites, although Burton was not a Catholic and this action later caused a rift between Isabel and some of Burton's friends. It has been suggested that the death occurred very late on 19 October and that Burton was already dead by the time the last rites were administered. On his religious views, Burton called himself an atheist, stating he was raised in the Church of England which he said was "officially (his) church".  Isabel never recovered from the loss. After his death she burned many of her husband's papers, including journals and a planned new translation of The Perfumed Garden to be called The Scented Garden, for which she had been offered six thousand guineas and which she regarded as his "magnum opus". She believed she was acting to protect her husband's reputation, and that she had been instructed to burn the manuscript of The Scented Garden by his spirit, but her actions have been widely condemned.  Isabel wrote a biography in praise of her husband.  The couple are buried in a remarkable tomb in the shape of a Bedouin tent, designed by Isabel, in the cemetery of St Mary Magdalen Roman Catholic Church Mortlake in southwest London. The coffins of Sir Richard and Lady Burton can be seen through a window at the rear of the tent, which can be accessed via a short fixed ladder. Next to the lady chapel in the church there is a memorial stained-glass window to Burton, also erected by Isabel; it depicts Burton as a mediaeval knight. Burton's personal effects and a collection of paintings, photographs and objects relating to him are in the Burton Collection at Orleans House Gallery, Twickenham.

how did he die?
heart attack.