Question

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

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 \(c = 68\) yd and \(a=32\) yd, and we want to find \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

\(b=\sqrt{68^{2}-32^{2}}=\sqrt{(68 + 32)(68 - 32)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(68+32 = 100\) and \(68 - 32=36\). Then \(b=\sqrt{100\times36}\).

Step3: Calculate square - root

\(b=\sqrt{100\times36}=\sqrt{100}\times\sqrt{36}=10\times6 = 60\) yd.

Answer:

60