Download Trigonometry Introduction

Trigonometry Introduction
Aims:
 To understand the effects of enlargements on shapes and the
properties of similar shapes.
 To be able to understand that the angles are conserved in similar
shapes and that the ratio of the side lengths is fixed for each
angle
 To be aware of the links between the ratio of side lengths and the
angles in a right angled triangle and the trigonometric rules.
Starter
Which are congruent and similar shapes? What makes the shapes
congruent and similar? What is the same and what is different between
similar shapes?
Activity 1
Look at similar triangles by cutting A4, A5, A6, A7 paper diagonally, they
will produce triangles with the same angle. Discuss what will happen if we
double the sides etc. What is the relationship between the sides, ratios,
decimals? Is this the same for all of these triangles?
Activity 2
Try a different set of triangle with the vertical and horizontal sides in a
ratio of 2:1 or 3:2 etc. Will you always get the same angles? Is the ratio
or decimal the same? How does the decimal change? Discover that each
angle has its own ratio.
Extension: does this ratio work for other pairs of sides? Hypotenuse and
adjacent, hypotenuse and opposite?
Plenary
Discuss the group’s findings and the connections between the different
triangles, sides, angles and ratios. Introduce the concepts of different
names for these ratios and the words Sine, Cosine and Tangent. To be
explored next lesson.
Helen Statton
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