Let's break down the problem step by step. The man starts at his house and follows these directions:

1. He walks 20 meters east.
2. Then, he turns south and walks 10 meters.
3. Next, he turns west and walks 35 meters.
4. Finally, he turns north and walks 5 meters.

To find the straight-line distance from his starting point (initial position) to his final position, we can use the Pythagorean theorem by finding the net east-west and north-south movements.

Step-by-step calculation:

1. East-West movement:

   • Initially, he walks 20 meters east.
   • Then, he walks 35 meters west.
   • Net east-west displacement = 35 m west - 20 m east = 15 m west.

2. North-South movement:

   • Initially, he walks 10 meters south.
   • Then, he walks 5 meters north.
   • Net north-south displacement = 10 m south - 5 m north = 5 m south.

Now, we can find the straight-line distance using the Pythagorean theorem, as the net displacement forms a right triangle: $\text{Straight-line distance} = \sqrt{(\text{east-west displacement})^2 + (\text{north-south displacement})^2}$ $\text{Straight-line distance} = \sqrt{(15)^2 + (5)^2} = \sqrt{225 + 25} = \sqrt{250} \approx 15.81 \, \text{m}$

Final Answer:

The straight-line distance between his initial and final positions is approximately 15.81 meters.

Would you like further details or have any questions about this solution?

Here are some related questions you could explore next:

1. What is the Pythagorean theorem and how is it used in real-life applications?
2. How would the straight-line distance change if he took a different route?
3. Can this problem be solved using vectors instead of the Pythagorean theorem?
4. What would the straight-line distance be if he walked further north instead of south?
5. How can we use coordinate geometry to solve such problems?

Tip: Always visualize the path using a simple diagram. It makes understanding the problem much easier and helps avoid mistakes in calculations.