The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.

The opposite side of a right-angled triangle is the side which is opposite the marked angle.

The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.

Sine and cosine ratios

Maths

Checking and securing understanding of similar triangles

Checking and securing understanding of Pythagoras' theorem

The unit circle

Scaling the right-angled triangle from the unit circle

Tangent ratio

Using the sine ratio

Using the cosine ratio

Using the tangent ratio

Choosing the right trigonometric ratio

Choosing an appropriate method for finding lengths of a triangle

Problem solving with trigonometry

In this unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In the future unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In the prior unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In this unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.

Trigonometry

Which side would we label as 'adjacent' to the non-right angle shown?

In a right triangle, if you are provided with θ and the adjacent side, which function would you use to find the hypotenuse? 

In a right triangle, if θ = 35ᵒ and the opposite side is 4 cm, what is the length of the hypotenuse to the nearest whole number? 

In a right triangle, if you are provided with θ and the opposite side, which function would you use to find the adjacent side? 

In a right triangle, if θ = 40ᵒ and the adjacent side is 9 cm, what is the length of the hypotenuse to the nearest whole number? 

In a right triangle, if θ = 50ᵒ and the hypotenuse is 12 cm, what is the length of the adjacent side to the nearest whole number? 

In a right triangle, if the hypotenuse is 25 cm and a second side is 15 cm, what is the length of the third side? (Use a calculator to help you.)

Yes, because their three angles correspond.

No, because you always need a side and two angles.

For this pair of triangles, can you determine whether they are similar without using side lengths?

In a right triangle, if the shortest sides are 40 cm and 96 cm, what is the length of the hypotenuse? (Use a calculator to help you.)

It is not possible to know whether the triangles are similar or not.

Which of the following statements is true for these triangles?

Would a triangle ABC with sides AB = 32cm, BC = 24cm, AC = 40cm be similar to the one shown in the diagram?

Sine and cosine ratios

Lesson outcome