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