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.

Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.

The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.

Using the cosine ratio

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

Sine and cosine ratios

Tangent ratio

Using the sine 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

Using triangle ABC, if θ = 38ᵒ and hypotenuse AB = 14 cm, what is the length of the adjacent side AC to 1 d.p. ?

What is the value of cos(20ᵒ) to 2 d.p. ?

Using triangle ABC, if θ = 38ᵒ and AC = 6 cm, what is the length of the hypotenuse AB to 1 d.p. ?

Using triangle ABC, if θ = 30ᵒ and AC = 12 cm, what is the length of the hypotenuse AB to 1 d.p. ?

Using triangle ABC, if θ = 30ᵒ and AC = 9 cm, what is the length of the hypotenuse AB to 1 d.p. ?

In a right triangle, if the hypotenuse is 75 cm and a second side is 60 cm, what is the length of the third side? (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?

In a right triangle, if the shortest sides are 7.5 cm and 18 cm, what is the length of the hypotenuse? (Use a calculator to help you.)

Would a triangle ABC with sides AB = 16cm, BC = 10cm, AC = 21cm be similar to the one shown in the diagram?

Would a triangle ABC with sides AB = 12 cm, BC = 9 cm, AC = 15 cm be similar to the one shown in the diagram?

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?

Using the cosine ratio

Lesson outcome