after going 80m from his house towards east,a person turns left and goes 20m,then turns right and moves 100m,then turns left and goes 60m,then turns right and goes 120m to reach the park.what is the distance between his house and the park
To find the distance between the person's house and the park, we can use the Pythagorean theorem.
Step 1: Going 80m towards the east.
The person moves 80m towards the east, so we can consider this as the horizontal distance.
Step 2: Turning left and going 20m.
By turning left and going 20m, the person moves vertically.
Step 3: Turning right and moving 100m.
The person turns right and moves 100m horizontally.
Step 4: Turning left and going 60m.
By turning left and going 60m, the person moves vertically.
Step 5: Turning right and going 120m.
Finally, the person turns right and moves 120m horizontally to reach the park.
To find the total distance, we need to calculate the horizontal and vertical distances separately, and then find the hypotenuse.
Horizontal distance = 80m + 100m + 120m = 300m
Vertical distance = 20m + 60m = 80m
Now, we can find the hypotenuse using the Pythagorean theorem:
Distance = sqrt((Horizontal distance)^2 + (Vertical distance)^2)
Distance = sqrt(300^2 + 80^2)
Distance = sqrt(90000 + 6400)
Distance = sqrt(96400)
Distance ≈ 310.33m
Therefore, the distance between the person's house and the park is approximately 310.33 meters.
To find the distance between the person's house and the park, we can use the Pythagorean theorem.
Let's break down the directions into steps:
1. Going 80m towards the east.
2. Turning left and going 20m.
3. Turning right and going 100m.
4. Turning left and going 60m.
5. Turning right and going 120m to reach the park.
Now, let's find the north-south and east-west components of the distance traveled.
The person goes 80m east, then 20m north, then 100m west, then 60m south, and finally 120m east.
North-south component: 20m (north) - 60m (south) = -40m
East-west component: 80m (east) - 100m (west) + 120m (east) = 100m
Now, we can use the Pythagorean theorem:
Distance = √(north-south component)^2 + (east-west component)^2
Distance = √((-40)^2 + 100^2)
Distance = √(1600 + 10000)
Distance = √11600
Distance ≈ 107.74m
Therefore, the distance between the person's house and the park is approximately 107.74 meters.
east 80 + 100 + 120 = 300
north 20 + 60 = 80
sqrt (300^2 + 80^2) = 310