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

Problem solving with trigonometry

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

Choosing an appropriate method for finding lengths of a triangle

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

Isosceles triangle ABC has base 4 cm and ∠ABC = ∠BCD = 30ᵒ. What is the height of the triangle to 2 d.p. ?

Isosceles triangle ABC has base 9 cm and ∠ABC = ∠BCD = 42ᵒ. What is the height of the triangle?

What is the area of an equilateral triangle of side 4 cm to 2 d.p. ?  

Isosceles triangle ABC has base 4 cm and ∠ABC = ∠BCD = 20ᵒ. What is the area of the triangle to 2 d.p. ?

Isosceles triangle ABC has base 5 cm and ∠ABC = ∠BCD = 24ᵒ. What is the perimeter of the triangle to 2 d.p. ?

A yacht sails 50 km due East and then 60 km due South. If the yacht is still facing South, how many degrees clockwise (2d.p.) should it turn to be facing directly towards its starting point.

In a right triangle, if the shortest sides are 48 cm and 20 cm, what is the length of the hypotenuse?

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 hypotenuse is 45 cm and a second side is 36 cm, what is the length of the third side? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 15 cm and a second side is 12 cm, what is the perimeter? (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?

Could an equilateral triangle be similar to the triangle below?

Problem solving with trigonometry

Lesson outcome