Revision notes for Foundation and Higher. Three ideas, each with a worked example, the reason for every line, and the trap to avoid.
Every worked example was checked by the code that marks Mathable’s tests.
1Spot the hypotenuse
The hypotenuse is the longest side, opposite the right angle, never one of the two shorter sides.
Think of it like
Picture the right angle as a corner; the hypotenuse is the slanting side leaning away from that corner.
Worked example
A right-angled triangle has sides 9 cm, 12 cm and 15 cm. The right angle is between the 9 cm and 12 cm sides. Find the length of the hypotenuse, in cm.
hypotenuse is opposite the right anglefind the side facing it
not 9 cm or 12 cm, so it is 15 cmthe only side left
Answer
TrapIf you pick the longest-looking side without checking it faces the right angle, you can choose wrong.
Explain it back
Why must the hypotenuse be the side facing the right angle?
Say it out loud in two or three sentences. Where you get stuck is what to revise.
2Add or subtract?
Add squares to find the hypotenuse, subtract squares to find a shorter side.
Think of it like
The hypotenuse is the biggest piece, so it always holds the sum of the other two squares.
Worked example
A right-angled triangle has a hypotenuse of 26 cm and one shorter side of 10 cm. Find the length of the other shorter side, in cm.
hypotenuse known, subtract
square the given sides
undo the square
Answer
TrapIf you add the squares instead of subtracting, you get a side longer than the hypotenuse.
Explain it back
Why must you subtract here instead of adding?
3Round only at the end
Keep the full decimal on your calculator and round only your final answer.
Think of it like
Think of carrying a full glass of water to the end, not spilling drops by rounding too soon.
Worked example
A right-angled triangle has shorter sides 7 cm and 10 cm. Find the length of the hypotenuse, in cm, to 1 decimal place.
add the squares
undo the square
Answerx ≈ 12.2round final answer
TrapIf you round √149 to 12 before stating the answer, your final figure loses accuracy.
Explain it back
Why should you round only the last line of working?
Practise with Mathable
Practise Pythagoras with a tutor that checks every line
›Ten questions on Pythagoras, marked for you.
›It points at the first mistake in your working.
›One hint at a time, so you work out the fix yourself.
›Explain an idea back, and it tells you the one gap.
