Driving Question: How far does the x-y pattern generator or barcode scanner, have to be placed from a two-dimensional barcode (a QR code) to properly read it?
Synopsis: Barcode scanners need to scan the entire area of a barcode to properly read it. The x-y pattern generator used in this lesson displays a pattern at a fixed angle, the amount of area that it can cover is dependent on how far away the x-y pattern generator is from the barcode. Students will determine how far away the x-y pattern generator needs to be placed in order to properly scan a QR code. Students will apply their knowledge of congruence and similarity criteria for triangles to find the ratio between the size of the x-y pattern and distance from the x-y pattern generator.
Common Core Math Standards: Students will
Prove theorems involving similarity
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Apply trigonometry to general triangles.
Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
MCC OPT 110 Topics:
How Light Behaves – reflection
Light in Technology and Industry – Lasers (barcode scanners)