Sure, let's break down the problem and answer each part step by step.
### Part (a): Draw the situation
1. Start by drawing a point to represent the starting spot.
2. Draw a straight line towards the right (eastwards) to represent the 10 km walk east.
3. From the end of this line, draw another line at a bearing of 110 degrees for 8 km. Remember that bearings are measured clockwise from the north. So, you will need to draw a line that goes 110 degrees clockwise from the north direction, but originating from your current position.
### Part (b): Calculate the distance directly south
To find out how far directly south the man is from his starting spot, we can break the problem into components.
1. He first walks 10 km east; this doesn't influence the south/north distance.
2. When he walks 8 km at a bearing of 110 degrees, we can decompose this movement into east and south components using trigonometry. The south component can be calculated using the sine function of the bearing angle.
The south component is approximately 7.52 km.
### Part (c): Calculate the distance directly east
To find out how far directly east the man is from his starting spot:
1. He initially walks 10 km east.
2. The eastward component of the 8 km walk at a bearing of 110 degrees is found using the cosine function of the bearing angle.
Combining the initial 10 km and the eastward component of the second leg, the total east distance is approximately 7.26 km.
So, summarizing the results:
- Directly south from the starting spot: 7.52 km
- Directly east from the starting spot: 7.26 km
