randRange(3, 8) randRange(3, 8) AC * AC + BC * BC

In the right triangle shown, AC = AC and BC = BC.

What is AB?

betterTriangle( BC, AC, "A", "B", "C", BC, AC, "?" );
AB2

We want to find c; let a = BC and b = AC.

\begin{align} c^2 &= BC^2 + AC^2 \\ c^2 &= BC * BC + AC * AC \\ c^2 &= AB2 \\ c &= \sqrt{AB2} \end{align}

Simplifying the radical gives c = formattedSquareRootOf(AB2).

So c = formattedSquareRootOf(AB2).

The radical cannot be simplified, so c = 1\sqrt{AB2} or just \sqrt{AB2}.

randRange(3, 5) randRange(6, 10) AB * AB - AC * AC shuffle([["a", "?", "BC", sqrt(BC2)], ["b", AC, "AC", AC]]) legs[0] legs[1]

In the right triangle shown, bside = AC and AB = AB.

What is aside?

betterTriangle( alen, blen, "A", "B", "C", alabel, blabel, AB );
BC2

We want to find a; let b = AC and c = AB.

So a^2 = c^2 - b^2

\begin{align} a^2 &= AB^2 - AC^2 \\ a^2 &= AB * AB - AC * AC \\ a^2 &= BC2 \\ a &= \sqrt{BC2} \end{align}

Simplifying the radical gives a = formattedSquareRootOf(BC2).

So aside = formattedSquareRootOf(BC2).

The radical cannot be simplified, so aside = 1\sqrt{BC2} or just \sqrt{BC2}.

We know a^2 + b^2 = c^2.