Question

15.) a= 22, b= ???, c= 25

Explanation:

Assuming this is a right - triangle problem where we use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (if \(c\) is the hypotenuse) or \(b^{2}+a^{2}=c^{2}\) (depending on the sides), or \(c^{2}-a^{2}=b^{2}\) if \(c\) is the hypotenuse and \(a\) is a leg.

Step 1: Identify the formula

Assuming it's a right triangle with \(c\) as the hypotenuse, we use the Pythagorean theorem \(b=\sqrt{c^{2}-a^{2}}\) (if \(b\) is a leg).

Step 2: Substitute the values

Given \(a = 22\) and \(c=25\), we substitute into the formula: \(b=\sqrt{25^{2}-22^{2}}\)
First, calculate \(25^{2}=625\) and \(22^{2} = 484\)
Then, \(25^{2}-22^{2}=625 - 484=141\)
So, \(b=\sqrt{141}\approx11.87\) (if we assume \(b\) is a leg)

If \(b\) is the hypotenuse, then \(b=\sqrt{a^{2}+c^{2}}=\sqrt{22^{2}+25^{2}}=\sqrt{484 + 625}=\sqrt{1109}\approx33.3\)

But usually, if \(c\) is given as 25 and \(a = 22\), and \(c>a\), \(c\) is more likely the hypotenuse. So the most probable value of \(b\) (as a leg) is \(\sqrt{141}\approx11.87\)

Answer:

If \(c\) is the hypotenuse, \(b=\sqrt{25^{2}-22^{2}}=\sqrt{141}\approx11.87\); if \(b\) is the hypotenuse, \(b=\sqrt{22^{2}+25^{2}}=\sqrt{1109}\approx33.3\). The more probable value (assuming \(c\) is hypotenuse) is \(\sqrt{141}\approx11.87\)