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A person desires to reach a point 3.42km from her present location and in a direction that is 35° north of east however she must travel along the street that go either north south or east west what is the minimum distance she could travel to reach on destination
The vector with initial point at her present position and terminal point at her desired position is v = ||v||( cosΘ i + sinΘ j ) = 3.42 cos(35°) i + 3.42 sin(35°) j. The minimum distance traveled with the given restrictions is along the legs 3.42 cos(35°) in the east-west direction and 3.42 sin(35°) in the north-south. It doesn't matter which she does first. No other path is minimum because any other path would require over shooting her target and doubling back---not smart if you want the shortest route! So the distance is 3.42 cos(35°) + 3.42 sin(35°) ≈ 4.74 km
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