We are given a right triangle with hypotenuse of length 6 km, an angle of 30 degrees, and the opposite side to this angle is $x = 3$ km. We need to find the length of the adjacent side (adj) to the 30 degree angle to 3 decimal places.

1. Problem Description

We are given a right triangle with hypotenuse of length 6 km, an angle of 30 degrees, and the opposite side to this angle is $x = 3$ km. We need to find the length of the adjacent side (adj) to the 30 degree angle to 3 decimal places.

2. Solution Steps

Let the length of the adjacent side be denoted by $a$.

We can use the cosine function:

$cos(\theta) = \frac{adjacent}{hypotenuse}$

$cos(30^{\circ}) = \frac{a}{6}$

$a = 6 * cos(30^{\circ})$

We know that $cos(30^{\circ}) = \frac{\sqrt{3}}{2}$.

So, $a = 6 * \frac{\sqrt{3}}{2} = 3\sqrt{3}$.

We want to approximate $a$ to 3 decimal places.

We know $\sqrt{3} \approx 1.73205080757$.

$a = 3 * \sqrt{3} \approx 3 * 1.73205080757 \approx 5.19615242271$.

Rounding to 3 decimal places, we get $a \approx 5.196$.

3. Final Answer

$5.196$