Question

determine the length of side \\(\overline{st}\\). round to the nearest tenth, if necessary.\\(\text{ }\\)\\(\text{ }\\)\\(st = \boxed{\text{ }} \text{ units}\\)

Explanation:

Step1: Identify the triangle type

This is a right - triangle with right angle at \(S\), hypotenuse \(RT = 14.7\) and one leg \(RS=8.2\). We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Let \(ST = x\), \(RS = 8.2\) and \(RT=14.7\). So \(RS^{2}+ST^{2}=RT^{2}\), then \(ST=\sqrt{RT^{2}-RS^{2}}\)

Step2: Substitute the values

\(RT = 14.7\), \(RS=8.2\), so \(RT^{2}=14.7^{2}=216.09\), \(RS^{2}=8.2^{2} = 67.24\)
Then \(RT^{2}-RS^{2}=216.09 - 67.24=148.85\)

Step3: Take the square root

\(ST=\sqrt{148.85}\approx12.2\) (rounded to the nearest tenth)

Answer:

\(12.2\)