Use Pythagoras’ theorem to find a missing side, in triangles, ladders and between points on a grid.
What you practise
Finding the longest side
Finding a shorter side
Distance between two points
Builds from whole-number triangles to answers rounded to one decimal place. Practice moves up a level when a round goes well and down when it does not.
Sample questions
Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.
Sample question, level 2 of 5
Find the other shorter side of a right-angled triangle with a longest side of 85 cm and one shorter side of 13 cm.
98 cm
72 cm
7056 cm
86 cm
84 cm
Show the answer and method
Answer: E, 84 cm
The method: 85² − 13² = 7225 − 169 = 7056, and √7056 = 84 cm.
Why the other options are wrong:
A, 98 cm: The sides were added.
B, 72 cm: The sides were subtracted. Square them, subtract the squares, then take the square root.
C, 7056 cm: The square root was not taken at the end.
D, 86 cm: The squares were added. To find a shorter side, subtract.
Sample question, level 4 of 5
A ladder 97 m long leans against a vertical wall. It reaches 65 m up the wall. How far is the foot of the ladder from the wall?
116.8 m
72 m
162 m
5184 m
32 m
Show the answer and method
Answer: B, 72 m
The method: The ladder is the longest side: 97² − 65² = 9409 − 4225 = 5184, and √5184 = 72 m.
Why the other options are wrong:
A, 116.8 m: The squares were added. The ladder is the longest side, so subtract.
C, 162 m: The lengths were added.
D, 5184 m: The square root was not taken at the end.
E, 32 m: The lengths were subtracted. The ladder, wall and ground make a right-angled triangle.
