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Pythagoras’ theorem
Finding the hypotenuse and shorter sides with Pythagoras' theorem, exact surd answers, and solving two-dimensional problems.
The theorem
$c$ is the hypotenuse, the longest side, opposite the right angle.
Drag P. Its x and y values are the two shorter sides of a right-angled triangle; the hypotenuse runs from the origin to P.
Find the hypotenuse of a right-angled triangle with sides $9$ and $12$.
A $5$ m ladder has its foot $1.4$ m from a wall. How high up the wall does it reach?
Find the hypotenuse for sides $9$ and $12$.
$\sqrt{225}$.
A $5$ m ladder stands $1.4$ m from a wall. Height reached (m)?
$\sqrt{23.04}$.
Hypotenuse $13$, one side $5$. Find the other side.
$\sqrt{169 - 25}$.
Find the diagonal of an $8$ cm by $6$ cm rectangle.
$\sqrt{100}$.
The exact hypotenuse for sides $4$ and $7$ is:
$16 + 49 = 65$.
A square has diagonal $\sqrt{128}$. Find its side length.
$2s^2 = 128$, so $s^2 = 64$.
Is a triangle with sides $7, 24, 25$ right-angled?
$49 + 576 = 625 = 25^2$.
Walk $5$ km east then $3$ km south. How far from the start (2 decimal places)?
$\sqrt{34}$.
New numbers every time. Keep going until you get five in a row.