Worked example 1 Identify the hypotenuse, opposite and adjacent in the following triangles. (i)
(ii) A θ Solution (ii) hypotenuse.
opposite. adjacent.
opposite hypotenuse adjacent hypotenuse.
opposite. adjacent
adjacent hypotenuse opposite
Discuss and discover
Work with a classmate to complete the following task. (i) Construct three different right-angled triangles with an angle of 30°, as shown. (ii) Measure the length of the hypotenuse and the other two sides. (iii) Copy and complete the table below to fi nd a relationship between each pair of sides. (v) What do you notice? (vi) Repeat (i), (ii) and (iii) for an angle of 60°.
(vii) Write a statement to apply your fi ndings to all situations (generalise your fi ndings). Length of
hypotenuse
Triangle 1 Triangle 2 Triangle 3
Length of opposite
30°
Length of adjacent
_ hyp
opp
_ hyp
adj
_ adj
opp
Express the answers as decimals correct to two places.
Having completed the activity above, we can see that each ratio is dependent purely on the angle – regardless of the size of the triangle. Therefore, the ratios of the sides remain the same.