Question

1. 9) s 4 yd ? t 1 yd u st =

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(STU\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = SU=4\) yd (hypotenuse), \(b = TU = 1\) yd, and \(a=ST\). So \(ST^{2}+TU^{2}=SU^{2}\), which can be rewritten as \(ST^{2}=SU^{2}-TU^{2}\).

Step2: Substitute the values

Substitute \(SU = 4\) and \(TU = 1\) into the formula \(ST^{2}=SU^{2}-TU^{2}\). Then \(ST^{2}=4^{2}-1^{2}\).

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Step3: Solve for \(ST\)

Take the square root of both sides. Since \(ST>0\) (length), \(ST=\sqrt{15}\approx 3.87\) yd.

Answer:

\(\sqrt{15}\text{ yd}\approx3.87\text{ yd}\)