Idea 2of 6Builds onTwo arrows, one path
North part, east part
One slanted arrow. How much of it points north?
Today you'll discover
- why a slanted arrow is really two straight ones
- cutting an arrow into a north part and an east part
- why the two parts rebuild the arrow exactly
Think firstA hundred-kilometre road, tilted from north toward east
The road is a hundred kilometres long and tilted toward east. How much of it points north?
Decide first, then press Next. Watch the slanted arrow become a north piece and an east piece.
A compass rose, north up. After a prediction, a hundred-kilometre arrow tilted from north toward east is shown; a dashed line drops from its head to the north axis, marking its north part, and a dashed line along the bottom marks its east part; both are named. The last step cuts the hiker's eighteen-kilometre arrow into its ten-north and fifteen-east parts.
See the whole ideathe big idea and the key word, in one place
The big idea
Any arrow is a north part and an east part: components.
See the patternAn arrow of size v tilted an angle θ from north has a north part of v cos θ and an east part of v sin θ. The two parts and the arrow make a right-angled triangle, which is why the arrow's size is the square root of the parts squared and added.
Key word
- component
- the part of a vector along one chosen axis; the north and east components of an arrow add tail to head to rebuild it
About this modelArrows are drawn to the scale in the corner; a bearing turns from north (or east).
Arrows are drawn to the scale in the corner; a bearing turns from north (or east).
Ready to use it?
- Split a described vector into its north and east components.