Find the hypotenuse or a shorter side of a right-angled triangle, check whether a triangle has a right angle, and find the distance between two points.
What you will learn
- Find the hypotenuse of a right-angled triangle
- Find a shorter side
- Decide whether a triangle is right-angled
- Find the distance between two points
- Use Pythagoras in ladders, fields and other contexts
Square the two short sides and add
In a right-angled triangle the longest side is opposite the right angle.
It is called the hypotenuse. Pythagoras' theorem says the squares of the two shorter sides add up to the square of the hypotenuse.
a² + b² = c²
- shorter sides 6 cm and 8 cm, hypotenuse x
- x² = 6² + 8² = 36 + 64 = 100
- x = √100 = 10 cm
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Square the two short sides and add
- Finding a shorter side: subtract
- Right angle or not, and distances on a grid
- Pythagoras in problems
- Try it: An easy one first
8 practice questions, marked as you go; about 25 minutes in all.
Key terms
Hypotenuse
In this unit: Pythagoras and trigonometry
Pythagoras' theorem, sin, cos and tan in right-angled triangles, angles of elevation, depression and bearings, exact values, 3D problems, and the sine and cosine rules.