Question

learn with an example
what is the length of the missing leg? if necessary, round to th
a = kilometers
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Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse (\(c = 30\) km) and \(b=18\) km. We need to find \(a\). Rearranging the formula gives \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 30\) and \(b = 18\) into the formula: \(a=\sqrt{30^{2}-18^{2}}=\sqrt{(30 + 18)(30 - 18)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). Then \(a=\sqrt{48\times12}=\sqrt{576}\).

Step3: Calculate the square root

\(\sqrt{576}=24\).

Answer:

\(24\)