Question

1. 13in. missing side=_in. 12in. 3) 5cm missing side=_cm 6cm 4) 10m 15m missing side=___m

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). If we know two sides and need to find the third, we can rearrange the formula.

Step2: Solve for problem 2

Let the hypotenuse \(c = 13\) in and one side \(a = 12\) in. We want to find the other side \(b\). Using \(b=\sqrt{c^{2}-a^{2}}\), we have \(b=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25}=5\) in.

Step3: Solve for problem 3

Let the two legs of the right - triangle be \(a = 5\) cm and \(b = 6\) cm. We want to find the hypotenuse \(c\). Using \(c=\sqrt{a^{2}+b^{2}}\), we have \(c=\sqrt{5^{2}+6^{2}}=\sqrt{25 + 36}=\sqrt{61}\approx 7.81\) cm.

Step4: Solve for problem 4

Let the hypotenuse \(c = 15\) m and one side \(a = 10\) m. We want to find the other side \(b\). Using \(b=\sqrt{c^{2}-a^{2}}\), we have \(b=\sqrt{15^{2}-10^{2}}=\sqrt{225 - 100}=\sqrt{125}=5\sqrt{5}\approx 11.18\) m.

Answer:

1. 5
2. \(\sqrt{61}\)
3. \(5\sqrt{5}\)