- Use the pythagorean theorem to solve right triangles
Pythagorean Theorem
In a right triangle, the sides have a special relationship described by the Pythagorean Theorem:
[latex]a^2 + b^2 = c^2[/latex]
where [latex]a[/latex] and [latex]b[/latex] are the legs, and [latex]c[/latex] is the hypotenuse (the side opposite the right angl
This relationship lets us find any missing side of a right triangle when we know the other two.
Find the hypotenuse of a right triangle with legs [latex]a = 6[/latex] and [latex]b = 8[/latex].
[latex]\begin{align} a^2 + b^2 &= c^2 \[4pt] 6^2 + 8^2 &= c^2 \[4pt] 36 + 64 &= c^2 \[4pt] 100 &= c^2 \[4pt] c &= \sqrt{100} = 10 \end{align}[/latex]
Result: [latex]c = 10[/latex]
Find a missing leg when [latex]b = 9[/latex] and [latex]c = 15[/latex].
[latex]\begin{align} a^2 + b^2 &= c^2 \[4pt] a^2 + 9^2 &= 15^2 \[4pt] a^2 + 81 &= 225 \[4pt] a^2 &= 144 \[4pt] a &= 12 \end{align}[/latex]
Result: [latex]a = 12[/latex]