Question

Village W is 20 km to the North of village X. Village Y is 18 km to the East of village X. Village Z is 12 km to the West of W. If Manu starts from village Y and goes to village Z via village W, in which direction is he from his starting point ?​

Answer 1

Answer:

You can see the answer in adjoining pic.

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Answer 2

Manu is 12.03 degrees West of North from his starting point.

To determine the direction Manu is from his starting point, we need to find the relative direction from village Y to village Z via village W.

First, we can draw a diagram to represent the positions of the four villages:

       Y

       |

       |

X-------W-------Z

       |

       |

       |

       |

From the diagram, we can see that Manu needs to travel 20 km North from Y to reach W, then 12 km West from W to reach Z. Therefore, the total distance Manu needs to travel is 20 + 12 = 32 km.

To find the direction, we can use trigonometry. The angle between the North direction and the line from Y to W is given by:

$tan(theta) = (18 km) / (20 km)$

$theta = arctan(0.9) = 42.99 degrees$

The angle between the West direction and the line from W to Z is given by:

$tan(phi) = (12 km) / (20 km)\\phi = arctan(0.6) = 30.96 degrees$

To find the relative direction from Y to Z, we can subtract the angle phi from theta:

$theta - phi = 12.03 degrees$

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