Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth. c = kilometers

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 5.3\) km and \(b = 5.3\) km. So \(c^{2}=(5.3)^{2}+(5.3)^{2}\).

Step2: Calculate \((5.3)^{2}+(5.3)^{2}\)

\((5.3)^{2}=5.3\times5.3 = 28.09\), then \((5.3)^{2}+(5.3)^{2}=28.09 + 28.09=56.18\). So \(c^{2}=56.18\).

Step3: Find \(c\)

\(c=\sqrt{56.18}\approx7.5\) (rounded to the nearest tenth).

Answer:

\(7.5\)