Question

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

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(a = 2.7\) km, \(b = 5.3\) km and \(c\) is the hypotenuse. So \(c=\sqrt{a^{2}+b^{2}}=\sqrt{2.7^{2}+5.3^{2}}\).

Step2: Calculate squares

First, calculate \(2.7^{2}=2.7\times2.7 = 7.29\) and \(5.3^{2}=5.3\times5.3 = 28.09\).

Step3: Sum the squares

Then, \(7.29 + 28.09=35.38\).

Step4: Find square - root

\(c=\sqrt{35.38}\approx5.9\) km.

Answer:

5.9