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.

Using Pythagoras' theorem to justify a right-angled triangle

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

...the longest edge is called the hypotenuse.

...the other two angles are $$45^\circ$$.

If a triangle is right-angled this means...

If a triangle is right-angled then $$a^2+b^2=c^2$$ where...

Impossible to tell, as we haven't got a diagram.

A triangle has these three edge lengths: 13 cm, 18cm and 31 cm. Is it a right-angled triangle?

No, you cannot have a right-angled isosceles triangle.

Impossible to tell, as isosceles triangles can have many different angles.

An isosceles triangle has these three edge lengths: $$19\sqrt{2}$$ cm, $$19\sqrt{2}$$ cm and 38 cm. Is it a right-angled triangle?

Here is a plan view of a room. There are two external walls; are they perpendicular?

Which of these triangles ABC, are right-angled?

Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a __________ triangle is equal to the square of the hypotenuse.

9.32 cm (rounded to 3 significant figures)

9.32738 (rounded to 5 significant figures)

A trapezium is formed by a right-angled triangle and a rectangle. Work out the length of the edge marked $$x$$.

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