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

Choosing an appropriate method for finding lengths of a triangle

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 cosine ratio

Using the tangent ratio

Choosing the right trigonometric ratio

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

This robot standing on a box has a fly on the top of their head. How high up (h) is the fly from the ground?

This robot standing on a box has an ant on the top of their head. How high up (h) is the ant from the ground to 2 d.p. ?

If the area of square ABCD is $$25 cm^2$$, what is the length of the diagonal BD to 2 d.p. ? 

A rectangle ABCD has length 6cm, and the diagonal angle ABC is 38ᵒ. What is the height of the rectangle to 2 d.p. ? 

A rectangle ABCD has length 12cm, and the diagonal angle ABC is 40ᵒ. What is the area of the rectangle to 2 d.p. ? 

Given all angles and the base of an isosceles triangle, what trigonometric function could be used to find the height of the triangle most efficiently?

In a right triangle, if the hypotenuse is 40 cm and a second side is 32 cm, what is the length of the third side? (Use a calculator to help you.)

In a right triangle, if the shortest sides are 10 cm and 7.5 cm, what is the length of the hypotenuse? (Use a calculator to help you.)

Would a triangle ABC with sides AB = 9cm, BC = 7.5cm, AC = 12.5cm 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?

In a right triangle, if the hypotenuse is 200 cm and a second side is 120 cm, what is the perimeter? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 30 cm and a second side is 18 cm, what is the area? (Use a calculator to help you.)

Choosing an appropriate method for finding lengths of a triangle

Lesson outcome