Gradient and Tangent

Australian curriculum number (ACMMG224; ACMNA294)

Students make links between gradient and angle by applying their understanding of the tangent ratio to find the actual angles represented by a road grade sign or the angle of a street.

This sequence is for students who:

  • can use the three basic trigonometric ratios to find unknown angles.
  • are familiar with plotting points and lines on the Cartesian plane.


Lesson 1: How Steep is That?

Students are presented with examples of road grade signs, research what is a road grade and determine the actual angle of a road when given its grade. Students then construct their own road sign using the actual angle of elevation, and confirm their understanding by creating a sign for a ramp or slope around their school.

Lesson 2: The World’s Steepest Street

Students use photos and YouTube videos of Baldwin Street, in New Zealand (the steepest street in the world at the time of publishing) to find the angle of elevation and tangent ratio of the street, then model the road system on a Cartesian plane. They analyse the elevation profile of the street and assess the accuracy of claims made about Baldwin Street.


Last updated June 21 2020.