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Draws a triangle based on 3 side lengths and randomises asking for hypotenuse or not.
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\\n
Give your answer correct to 1 decimal place.
Given a right angled triangle with perpendicular sides $ \\\\var{ac} cm$ and $\\\\var{bc} cm$, calculate the length of the unlabelled side.
Give your answer correct to 1 decimal place.
Avoid using rounded values in calculations and just round for the final answer.
Pythagoras Theorem states that, in a right angled triangle, with hypotenuse $c$:
\\\\[a^2 + b^2 = c^2\\\\]
\\nLet\\'s call the unknown value $x$, therefore we can write:
\\n$a = \\\\var{bc}$, $b =\\\\var{ac}$ and $c = x$
\\nSo
\\\\[\\\\var{bc}^2 + \\\\var{ac}^2 = x^2\\\\]
equivalently,
\\n\\\\[x^2 =\\\\var{bc}^2 + \\\\var{ac}^2\\\\]
\\nand therefore
\\n\\\\[x^2 = \\\\var{bc^2} + \\\\var{ac^2}\\\\]
\\\\[x = \\\\sqrt{\\\\var{bc^2} + \\\\var{ac^2}}\\\\]
\\\\[x = \\\\sqrt{\\\\var{bc^2+ac^2}}\\\\]
$x = \\\\var{ab}$ to 1dp.
Avoid using rounded values in calculations and just round for the final answer.
Pythagoras Theorem states that, in a right angled triangle, with hypotenuse $c$:
\\\\[a^2 + b^2 = c^2\\\\]
\\nLet\\'s call the unknown value $x$, therefore we can write:
\\n$a = x$, $b =\\\\var{ac}$ and $c = \\\\var{ab}$
\\nSo
\\n\\\\[x^2 + \\\\var{ac}^2 = \\\\var{ab}^2\\\\]
\\nand therefore
\\n\\\\[x^2 + \\\\var{ac^2} = \\\\var{ab^2}\\\\]
\\n\\\\[x^2 = \\\\var{ab^2} - \\\\var{ac^2}\\\\]
\\n\\\\[x = \\\\sqrt{\\\\var{ab^2-ac^2}}\\\\]
$x = \\\\var{bc}$ to 1dp.
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