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

Checking and further securing understanding of Pythagoras' theorem

Calculating the length of a line segment

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

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

...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 $$x$$.

Starter Quiz

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.