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two cars leave an intersection at the same time, one travelling at 70km/h along one road and the other car travelling at 80km/h along the other road. After 2 hours they are 218 km apart. At what angle, to the nearest minute, do the roads meet at the intersection.



Answer :

[tex]v_1=70\ km/h\\v_2=80\ km/h\\t=2h\\\\v=\frac{s}{t}\to s=vt\\\\s_1=70\ km/h\cdot2h=140\ km\\s_2=80\ km/h\cdot2h=160\ km\\\\look\ at\ the\ picture[/tex]


[tex]218^2=140^2+160^2-2\cdot140\cdot160\cdot cos\alpha\\\\47524=19600+25600-44800cos\alpha\\\\47524=45200-44800cos\alpha\\\\44800cos\alpha=45200-47524\\\\44800cos\alpha=-2324\ \ \ \ /:44800\\\\cos\alpha\approx-0.051875\Rightarrow\alpha\approx92^o58'[/tex]
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