Final answer:
Christopher Columbus mistakenly believed he had found a westward passage to Asia, when he actually discovered the Americas. Despite his navigational errors, he died thinking he had reached Asia. Pedro Cabral was the first explorer to claim Brazil for Portugal.
Step-by-step explanation:
The explorer who believed he had discovered a westward passage to Asia but had in fact arrived in the Americas was Christopher Columbus. Columbus made his exploratory voyages under the sponsorship of the Spanish crown. On October 12, 1492, Columbus reached land in the Bahamas, and then sailed to what he named Hispaniola, which is today known as the Dominican Republic and Haiti. Despite these discoveries, Columbus went to his grave thinking he had found a new route to Asia. Other explorers like Vasco da Gama made it to India by sailing around the Cape of Good Hope, thereby securing the trade routes to Asia that Columbus had sought. The full scale of Columbus's mistake came to light during the voyages of other explorers, including Ferdinand Magellan's circumnavigation of the globe, which showed just how vast the world truly was, contrary to Columbus's calculations.
On related matters, the first explorer to reach Brazil and claim it for the throne of Portugal was Pedro Cabral.