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

Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

Checking and securing understanding of Pythagoras' theorem

Maths

Checking and securing understanding of similar triangles

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

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

In a right triangle, if the shortest sides are 6 cm and 8 cm, what is the length of the hypotenuse?

$$a^2+b^2=c^2$$ is a formula for which type of triangle? 

Which formula below is a rearrangement of $$a^2+b^2=c^2$$?

In a right triangle, if the hypotenuse is 40 cm and a second side is 24 cm, what is the length of the third side? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 30 cm and a second side is 24 cm, what is the area? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 65 cm and a second side is 60 cm, what is the perimeter? (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?

Isosceles triangles are always similar to each other.

Equilateral triangles are always similar to each other.

Right triangles are always similar to each other.

Scalene triangles are always similar to each other.

Rectangles are always similar to each other.

Parallelograms are always similar to each other.

Squares are always similar to each other.

An isosceles triangle has an internal angle of 100ᵒ, what are the other two angles?

Checking and securing understanding of Pythagoras' theorem

Lesson outcome