# Activities

• • ##### Subject Area

• Mathematics: Algebra and Pattern: Algebra and Pattern
• Mathematics: Measurement: Measurement
• Mathematics: Geometry and Space: Geometry and Space
• Standard: National Curriculum 7-10: Measurement and Geometry: Shape
• Standard: National Curriculum 7-10: Measurement and Geometry: Geometric reasoning

• ##### Author Middle

60 Minutes

• ##### Device
• TI-Nspire™ CX
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

## Similar Signs #### Activity Overview

Students investigate the ratio between the opposite side and hypotenuse of a right angled triangle as the triangle is dilated. Once students identify the outcome they explore changes to the angle and estimate ratios for specific angles.

#### Objectives

Use similarity to investigate the constancy of the sine ratio for a given angle in right-angled triangles (ACMMG223)

#### Vocabulary

• Ratio
• Similarity
• Opposite (side)
• Adjacent (side)
• Hypotenuse
• Dilation

#### About the Lesson

Students adjust the dilation of a right-angled triangle and observe and record the ratio between the hypotenuse and opposite side. The ratio is then observed and recorded as the angle is changed. Similarity explains the constancy of the ratio under some conditions whilst trigonometry provides an insight to the variation of the ratio.