Grade 10: Grain Elevators

grain elevators

Two tall grain elevators in the distance appear to be the same height though it is known that one (B) is twice the height of the other (A). How can I walk towards them in such a way that they always appear to be the same height.

The students will start by guessing, but what’s really needed is a coordinate system and an equation. We want the locus of a point that is always twice as far from B as from A. It’s a perfect task for grade 10 students who are developing facility with triangle trig and coordinate geometry.

The answer is a circle. Is that a surprise?

Teacher manual
Student workbook