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

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.

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?

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Calculating the length of a line segment

Lesson outcome