Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 25\) mm, \(b = 24\) mm, and we need to find \(a\). So, \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute values

Substitute \(c = 25\) and \(b = 24\) into the formula: \(a=\sqrt{25^{2}-24^{2}}=\sqrt{(25 + 24)(25 - 24)}\) (using the difference - of - squares formula \(x^{2}-y^{2}=(x + y)(x - y)\)).

Step3: Calculate

\(a=\sqrt{(49)\times(1)}=\sqrt{49}=7\) mm.

Answer:

7