Question

1. 8 km 16 km x

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). Here, the hypotenuse \(c = 16\) km and one leg \(a = 8\) km, and the other leg is \(x\). We can re - arrange the formula to solve for \(x\): \(x=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute the values

Substitute \(c = 16\) and \(a = 8\) into the formula. First, calculate \(c^{2}-a^{2}\):
\(c^{2}-a^{2}=16^{2}-8^{2}=256 - 64=192\)

Step3: Calculate the square root

Now, find the square root of 192. We can simplify \(\sqrt{192}\) as follows:
\(\sqrt{192}=\sqrt{64\times3}=\sqrt{64}\times\sqrt{3}=8\sqrt{3}\approx8\times1.732 = 13.856\) km (if we want a decimal approximation) or we can leave it in exact form \(8\sqrt{3}\) km.

Answer:

If in exact form, \(x = 8\sqrt{3}\) km \(\approx13.86\) km (rounded to two decimal places)