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A person desires to reach a point that is 2.17 km from her present location and in a direction that is 29.6° north of east. However, she must travel along streets that are oriented either north-south or east-west. What is the minimum distance she could travel to reach her destination?

Respuesta :

LammettHash

She needs to move [tex]x[/tex] km in the east-west direction and [tex]y[/tex] km in the north-south direction so that

[tex]\sqrt{x^2+y^2}=2.17[/tex]

and

[tex]\tan29.6^\circ=\dfrac yx[/tex]

Solve the system to get

[tex]x=1.89\,\mathrm{km}[/tex]

[tex]y=1.07\,\mathrm{km}[/tex]

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