In 2005, when discussing the proposed border wall between the United States and Mexico, then- Arizona governor Janet Napolitano said, “You show me a fifty foot wall. I’ll show you a fifty-one foot ladder.” Politics aside, would a 51-foot ladder actually be long enough to climb a 50-foot wall?

In this lesson, students combine OSHA’s recommendations for ladder safety with the Pythagorean Theorem (Grade 8) or trigonometric ratios (Geometry) to explore how high you can really climb.

### Students will

• Read OSHA recommendation on safe ladder orientation, and interpret as a ratio (Grade 8) or angle (Geometry)
• Calculate the distance a ladder should be placed from the ground (Grade 8) or a safe ladder angle (Geometry)
• Apply the Pythagorean Theorem (Grade 8) or trigonometric ratios (Geometry) in order to calculate how high a ladder will reach
• Apply mathematics of ladder safety to other areas, e.g. fire trucks

### Before you begin

Given two sides of a right triangle, Grade 8 students should know how to use the Pythagorean Theorem to find the length of the third side. Given a side and angle, Geometry students should know how to use trigonometric ratios — sine, cosine, and tangent — to find the lengths of the missing sides.

Note: though the lesson does not specifically mention the proposed border wall between the United States and Mexico, the topic may come up. We’ve received feedback from teachers who had excellent conversations — involving both math and public policy — with their students, but also emails from teachers whose students acted less maturely. Before teaching the lesson, you might consider how it will resonate with your students, particularly those from immigrant backgrounds.