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.

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

Applying Pythagoras' theorem in 3D

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

Which of these are right-angled triangles?

Given that DE = 6 cm and EH = 15 cm, what is the length of DH, to 1 decimal place?

Given that BG = 9 cm and GE = $$7\sqrt{2}$$ cm, what is the length of BE, to 1 decimal place?

If AF, FE and FH are known, which other length do we need, in order to calculate the volume of this cuboid?

Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, work out the length of EH.

Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, the volume of the cuboid ABCDEFGH is {{}} $$\text{ cm}^3$$

The relationship between the hypotenuse and the two short sides on a right-angled triangle is known as {{}}' theorem.

Work out the the length of the hypotenuse, to 1 decimal place.

Work out the length of the third side of the triangle, to 3 significant figures.

A football pitch is 115 yards by 74 yards. What is the distance diagonally from one corner flag to the other? Give your answer to the nearest yard.

This lesson will be removed by end of Summer Term 2025.

Applying Pythagoras' theorem in 3D

Lesson outcome

This lesson will be removed by end of Summer Term 2025.