A Tale of Three Intersecting Lines
Two sides and the angle between them
Construct a triangle from two sides and the angle between them.
Now we're given two sides and the angle between them (the included angle). 4 cm, 60°, 3 cm means the 60° sits between the 4 cm side and the 3 cm side.
Construct ∆ABC with AB = 5 cm, AC = 4 cm and ∠A = 45°. ∠A is at the corner where the two given sides meet, so it is the included angle.
- Step 1: draw AB = 5 cm as the base.
- Step 2: at A, use a protractor to draw the other arm of a 45° angle.
- Step 3: measure 4 cm along that arm from A and mark C.
- Step 4: join BC.
No arcs and no trial and error: the angle fixed the direction of the second side straight away.
Practise: 3 cm, 75°, 7 cm · 6 cm, 25°, 3 cm · 3 cm, 120°, 8 cm. Is there any two sides and included angle that can't make a triangle? Try to find one as you draw.
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