Rashi walks

Question

Rashi starts walking from her house. She first walks 10 meters south. She then turns left and
walks 60 meters. Then she turns right and walks 30metres after which she makes another
right turn and walks a further 30 meters. In which direction and how many meters away is
Rashi from her house.

Answer 1

Hi Dan.

 

Rashi's path looks a little like this.

 

S

|

|

|_________________________

                                             |

                                             |

                                             |

                                             |

                                             |

                  F______________|

 

From start to finish she's 40 meters south (10 meters from the first segment and 30 meters from the second segment), and she's 30 meters east (she walked 60 meters east on her first turn then came 30 meters back).

 

You can make this into a right triangle with vertical leg 40 meters and horizontal leg 30 meters, then use the Pythagorean theorem to find the hypotenuse, which will be the distance.

 

The distance will be √(40^2 + 30^2) = 50 meters

 

To find the direction, use tangent inverse. The angle you want is right where S is.

 

S

|\

|  \

|    \

|___\F

 

The opposite side of S is 30 meters. The adjacent side of S is 40 meters.

 

arctan(30/40) = ~37 degrees

 

So she's 50 meters away, and her bearing is S 37º E.

 

Hope this helps.