Draw three rightangled triangles each with one angle

Draw three right-angled triangles, each with one angle of 30°. Measure each side to the nearest mm and fill in the table. triangle hypotenuse (side opposite the right angle) side opposite 30° angle 1 2 3 What do you notice about the ratio between the opposite and hypotenuse sides in each triangle? © www. teachitmaths. co. uk 2012 16571 1

You should have found that the ratio of opposite : hypotenuse is 1: 2 or ½. How can equilateral triangles explain why this is true? 60° 30° 2 cm 60° 1 cm © www. teachitmaths. co. uk 2012 2 cm 16571 2

Explore your calculator! Can you find a function which gives the answer ½ when you input 30? If you input © www. teachitmaths. co. uk 2012 sin 30 16571 you get ½. 3

‘Sin’ is short for sine. Sine is a function which relates an angle to its opposite and adjacent sides: hyp opp α adj © www. teachitmaths. co. uk 2012 16571 4

opp hyp α adj We can use sine to calculate a missing length in a triangle: x substitute values: 47 cm 62° rearrange for x: type into your calculator: cm © www. teachitmaths. co. uk 2012 16571 5

opp hyp α adj We can use sine to calculate a missing length in a triangle: 8. 6 cm substitute values: x 50° rearrange for x: type into your calculator: cm © www. teachitmaths. co. uk 2012 16571 6

Calculate the length of side x in each of these triangles: 43 x 20. 2 cm 87 cm x 6. 1 cm 5. 3 cm 28° 53° 60° x 8. 8 cm x 144. 6 cm ? 37° 32° 16. 7 cm © www. teachitmaths. co. uk 2012 16571 7