Why Are Castles So Tall?

In this module students explore indirect measurement by seeing how simple angle measure, height measurements, and tangent ratios can be used to calculate distances. The context of castles provides a historically relevant military purpose for the tallness of castles.

This module explores Himeji Castle in Japan, as well as other castles. Some of the concepts explored in this module include:

  • Angle measurements and alternate interior angles of parallel lines
  • Tangent ratios
  • Linear functions, in particular the functional relationship between a castle's height and its line of sight for a given angle

This module provides a nice blend of algebra and geometry topics and can be used in an algebra unit on linear functions, a geometry unit on tangent ratios, or even a pre-calculus lesson on tangent ratios and functions.

Math Concepts

  • Functions
  • Ratios and Rates
  • Triangles
  • Geometry

Learning Objectives

  • Define trig ratios
  • Solve problems involving trig ratios
  • Use linear functions to model real-world phenomena

Prerequisite Skills

  • The concept of a ratio
  • Basic properties of right triangles
  • Basic understanding of a functional relationship between two variables
Common Core Standards CCSS.MATH.CONTENT.6.RP.A.3, CCSS.MATH.CONTENT.8.F.B.4, CCSS.MATH.CONTENT.7.G.B.5
Lesson Duration 30 mins
Grade Range 7th - 10th Grade

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