Name two muslim-developed technologies that the europeans used to explore the east

The astrolabe and the quadrant were Muslim inventions. Both of them were used to measure the inclined position in the sky of a celestial body and, therefore, to determine the latitude, longitude and time of day. The Muslims developed these instruments to determinate the direction of the Mecca, to which they turn to pray, and times for prayers.  

Also, the Muslims were great travelers since their religion encourages them to seek God's creations across the world, because of their commercial activities and, of course, because of the Hajj (pilgrimage) to spread their religion. This allowed them to create very detailed maps of the known lands, the most advanced ones at the time, that the Europeans could use in their exploratory navigations.