With AutoCAD, there is always a half dozen ways to do something. The most standard way is after you picked your starting point of the line, activate the perpendicular snap, than move your moose over any line. When AutoCAD finds a entity (line, arc, circle, pline, etc) that the new line can be perpendicular to, a little square symbol will display at the meeting point. Select the point & you've got it.
Activate the perpendicular snap by either picking the perpendicular button from the Object Snap toolbar or do a right-click while holding the shift button to display the shortcut menu. You can also make the perpendicular snap continuously active from the Drafting Settings/Object Snap menu.
Mastering how to use osnaps is important for accurate design/drafting.
Hope that helps