Coaching Centre
Pythagoras’ theorem
The hypotenuse, Pythagoras' theorem c² = a² + b², finding the hypotenuse, Pythagorean triples, and testing whether a triangle is right-angled.
The theorem
The hypotenuse is the longest side of a right-angled triangle. It is opposite the right angle.
Drag A and B. The hypotenuse joins them. Try a = 6, b = 8, or a = 5, b = 12.
Find the hypotenuse when the other sides are $9$ cm and $12$ cm.
Find the hypotenuse when the other sides are $5$ m and $7$ m, to 2 decimal places.
Testing for a right angle
Find the hypotenuse when the other sides are $9$ and $12$.
$\sqrt{225}$.
Find the hypotenuse when the other sides are $5$ and $7$ (2 d.p.).
$\sqrt{74}$.
Find the hypotenuse when the other sides are $5$ and $12$.
$\sqrt{169}$.
Is a triangle with sides $7$, $24$, $25$ right-angled?
$49 + 576 = 625$.
Is a triangle with sides $6$, $7$, $9$ right-angled?
$36 + 49 = 85 \ne 81$.
Find the hypotenuse when the other sides are $6$ and $8$.
$\sqrt{100}$.
Find the diagonal of a $1$ m square (2 d.p.).
$\sqrt{2}$.
Find the hypotenuse when the other sides are $8$ and $15$.
$\sqrt{289}$.
New numbers every time. Keep going until you get five in a row.