Question

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

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 \(c = 87\) ft and \(a=60\) ft. We want to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 87\) and \(a = 60\) into the formula: \(b=\sqrt{87^{2}-60^{2}}=\sqrt{(87 + 60)(87 - 60)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(87+60 = 147\) and \(87 - 60=27\), then \(b=\sqrt{147\times27}=\sqrt{3969}\).

Step3: Calculate the square - root

\(b=\sqrt{3969}=63\) ft.

Answer:

63