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.

Calculating the length of a line segment

Maths

Checking and further securing understanding of Pythagoras' theorem

Using Pythagoras' theorem to justify a right-angled triangle

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

Put the length of these line segments in order, starting with the shortest.

What is the length of the line segment AB, to 1 decimal place?

Given that A(4, 7) and B(7, 11), what is the length of the line segment AB?

Given that A(-9, -9) and B(3, -4), what is the length of the line segment AB?

Find the length of line segment CD starting at the origin with midpoint (4, 2). Give your answer to 2 decimal places.

The coordinates (3, 8) translate to (7, 8). What is the change to the $$x$$-coordinate?

The coordinates (3, -8) translate to (7, 8). What is the change to the $$y$$-coordinate?

Work out the length of the hypotenuse, for this right-angled triangle.

Work out the length of the edge marked $$x$$, for this right-angled triangle.

M is the midpoint of a line segment AB. Given that A(4, 8) and B(6, 20), what are the coordinates of the midpoint M?

M is the midpoint of a line segment AB. Given that A(5, 9) and M(8, 5), what are the coordinates of B?

Calculating the length of a line segment

Lesson outcome