Activity Overview
Students investigate the ratio between the adjacent 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.
Note: Students should complete the “Similar Signs” activity first.
Objectives
National Curriculum Reference ACMMG223:
Use similarity to investigate the constancy of the cosine ratio for a given angle in right-angled triangles.
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 adjacent 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.