The goal of this lesson is for students to use their understanding of similarity to recognize that the ratio of the legs of a right triangle with a given acute angle is fixed. Students should leave the lesson wondering how the people who wrote the Americans with Disabilities Act guidelines knew what the ratio of two sides of a right triangle would be for a given angle, or what the angle would be for a given ratio.

Students have a chance to do a portion of the modeling cycle (MP4) as they consider all of the possible factors that make a ramp safe (railings, steepness, width, surface). They then focus on how to account for a single aspect (steepness) as they begin to design a ramp to accompany a specific set of stairs.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.