Question

what is the length of the missing leg? if necessary, round to the nearest tenth. b = meters

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here \(c = 58\) m and \(a = 40\) m. We want to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 58\) and \(a = 40\) into the formula: \(b=\sqrt{58^{2}-40^{2}}=\sqrt{(58 + 40)(58 - 40)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(58+40 = 98\) and \(58 - 40=18\). Then \(b=\sqrt{98\times18}=\sqrt{1764}\).

Step3: Calculate the square root

\(\sqrt{1764}=42\) m.

Answer:

42