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 \(a = 4.2\) km and \(b = 8.5\) km, the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=(4.2)^{2}+(8.5)^{2}\).

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\((4.2)^{2}=4.2\times4.2 = 17.64\) and \((8.5)^{2}=8.5\times8.5 = 72.25\). Then \(c^{2}=17.64 + 72.25=89.89\).

Step3: Find \(c\)

\(c=\sqrt{89.89}\approx9.5\) (rounded to the nearest tenth).

Answer:

9.5