# Weekly math problem: surveying

Are you as sharp as Alzar School students?  Let’s see:

Last Friday, the Geometry class spent their 40-minute class period tromping around in the snow with sticks, measuring tape, compasses, and notebooks.  The challenge was this:

Part A: Indirectly measure the width of the North Fork of the Payette River as it meanders past our campus.  But the river’s cold, so you aren’t allowed to cross it!  The measurement must be done entirely using the floodplain on campus and lines of sight.

Part B: Indirectly measure the height of that big old tree in front of the Depot.  But climbing to the tippy top of trees is scary!  Not allowed.

So what do you think?  Can you come up with a way to do it?  Here’s a hint: This week in geometry we are studying similar triangles and extended ratios of sides.  Indirect measurement means to measure distances related to our unknown length and use the rules of similarity to determine the width of a cold river or height of a big tree.  Trigonometry isn’t until the next unit, so we aren’t measuring any angles this time around.

-Dan Thurber

Math Teacher, Alzar School