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

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.

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?

Starter Quiz