Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Let \(a = 1.6\), \(c=2.7\), and we want to find \(b\). Then \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 1.6\) and \(c = 2.7\) into the formula: \(b=\sqrt{2.7^{2}-1.6^{2}}=\sqrt{(2.7 + 1.6)(2.7-1.6)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)). First, \(2.7+1.6 = 4.3\) and \(2.7 - 1.6=1.1\). Then \(b=\sqrt{4.3\times1.1}=\sqrt{4.73}\).

Step3: Calculate the square - root

\(\sqrt{4.73}\approx2.2\)

Answer:

\(2.2\)