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 further securing understanding of Pythagoras' theorem

Maths

Using Pythagoras' theorem to justify a right-angled triangle

Calculating the length of a line segment

Checking and securing understanding of the unit circle

Checking and securing understanding of sine ratio problems

Checking and securing understanding of cosine problems

Checking and securing understanding of tangent ratio problems

Calculate trigonometric ratios for 30° and 60°

Calculate trigonometric ratios for 0°, 45° and 90°

Applying trigonometric ratios in context

Applying Pythagoras' theorem in 3D

Applying trigonometric ratios in 3D

Advanced problem solving with right-angled trigonometry

In this unit, pupils have explored the trigonometric ratios for right-angled triangles in a variety of situations. In the future unit, pupils explore what can be done when we have a triangle that is not right-angled.

In the prior unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In this unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In this unit, pupils are introduced to a variety of situations where trigonometric ratios are required, such as 3-D problems and problems of elevation or depression.

Right-angled trigonometry

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

The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.

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

The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.

The opposite side of a right-angled triangle is the side which is opposite the marked 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 tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.

A cross-section is a 2D face made from cutting straight through any plane of a 3D object.

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

Right-angled trigonometry

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