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.

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