a hiker travels for 15km on a bearing of 210T how far south is he please show working

does 210T mean 210° ?

I made a sketch and have him going S30W for 15 km
I completed a right-angled triangle by joining the end point to the y-axis , letting your "how far south) distance be y

y/15 = cos30°
y = 15cos30 = appr 12.99 km

To calculate how far south the hiker is traveling, we can use trigonometry.

First, let's draw a diagram to understand the scenario:

```
N
|
|
| 15 km
|
W ____________|______________ E
|
|
|
|
|
|
|
|
S
```

Here, the hiker is traveling on a bearing of 210 degrees from the North (N).

To find out how far south the hiker is traveling, we need to find the component of their displacement that lies in the south direction.

We can do this by using the sine function, which relates the opposite side (south component) to the hypotenuse (total displacement) of a right triangle.

The formula for calculating the opposite side (south component) is:

Opposite side = Hypotenuse * sin(angle)

In this case, the angle is 30 degrees, which is the difference between 210 degrees (bearing) and 180 degrees (bearing towards the south).

So, the calculation would be:

Opposite side = 15 km * sin(30 degrees)

Using a scientific calculator, sin(30 degrees) is approximately 0.5.

Therefore, the calculation becomes:

Opposite side = 15 km * 0.5

Opposite side = 7.5 km

Hence, the hiker is traveling approximately 7.5 km south.

To find out how far south the hiker is traveling, we can use trigonometry. Here's how you can calculate it step by step:

1. Identify the bearing: The bearing of 210T indicates that the hiker is traveling at an angle of 210 degrees measured clockwise from the north direction.

2. Determine the component of movement: Since we want to find the distance traveled south, we need to find the component of the movement in the south direction. To do this, we can use trigonometric functions.

In a right-angled triangle, the side opposite the angle (in this case, the south direction) is the component we are looking for. The hypotenuse of the triangle (in this case, the total distance traveled) is given as 15 km.

3. Use trigonometry: We can use the sine function to find the required component.

The sine of a given angle (in this case, 210 degrees) is the ratio of the side opposite the angle to the hypotenuse.

So, we can say: sin(210) = Opposite / Hypotenuse

Rearranging the equation: Opposite = Hypotenuse * sin(210)

4. Substitute the values and calculate: Now we can substitute the given values into the equation and calculate it.

Opposite = 15 km * sin(210)
Opposite = 15 km * (-0.5) (since sin(210) is -0.5)

Opposite = -7.5 km

Therefore, the hiker is traveling 7.5 km to the south.