Suppose you waik 18.0m straight west and then 25.o m straight north. How far are you from your starting point and what is the compass direction of a line connecting your starting point to yourfinal position?

To find the distance and compass direction between your starting point and final position, we can use the Pythagorean theorem and trigonometry.

Firstly, let's draw a diagram to visualize the situation. We have a straight path of 18.0 m to the west and then another straight path of 25.0 m to the north.

```
N
|
| 25.0 m
|
------------
Start 18.0 m End
|
|
|
W
```

Now, using the Pythagorean theorem, we can find the distance between the starting point and final position.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, the distance between the starting point and final position can be found using the formula:

distance = √(18.0^2 + 25.0^2)

Calculating this gives us:

distance = √(324 + 625) = √949 = 30.79 m (rounded to two decimal places)

Therefore, the distance between your starting point and final position is approximately 30.79 meters.

Next, let's find the compass direction of the line connecting the starting point to the final position. To do this, we can use trigonometric ratios.

The compass direction can be determined by finding the angle between the line connecting the starting point and final position (line EF) and the north direction (line EN).

To find this angle, we can use the tangent (tan) function:

tan(θ) = opposite/adjacent

In this case, the opposite side is 25.0 m (line EN) and the adjacent side is 18.0 m (line NE).

So, tan(θ) = 25.0/18.0

Taking the inverse tangent or arctan of both sides, we find:

θ = arctan(25.0/18.0) = 54.46° (rounded to two decimal places)

Therefore, the compass direction of the line connecting your starting point to the final position is approximately 54.46 degrees north of west.