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Sandra_henson
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Tyro
Asked: 2021-04-09T10:52:47+00:00 In: ,

Polar Coordinate System

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A public hospital is located 50 km to the east and 30 km to the north of James’ residence. Use the polar coordinates to determine the direction and distance of James’ residence from the hospital.

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  2. acedstud
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    Let the distance of James’ residence from the hospital be r, then x=r\cos{\theta}=50 km and y=r\sin{\theta}=30 km.

    r=\sqrt{x^2+y^2}=\sqrt{50^2+30^2}=\sqrt{2500+900}=\sqrt{3400}\approx{58.3} km.

    \theta=\tan^{-1}\dfrac{y}{x}=\tan^{-1}\dfrac{30}{50}=\tan^{-1}0.6\approx31^o.

    Therefore, the distance of James’ residence from the hospital is about 58.3 km and the direction is 90^o+(90^o-31^0)=90^o+59^o=149^o counter clockwise.

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