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- anonymous

Two roads intersect at an angle of 48 degrees. A car and truck collide at the intersection and leave the scene of the accident. The car travels to the east at 100km/h while the truck goes north at 80 km/h. Fifteen mins after the accident a police helicopter pulls over the car. Twenty mins after the accident a police cruiser pulls over the truck. How far apart are the car and truck at this time?

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- anonymous

- schrodinger

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- ash2326

See the picture

- ash2326

Car travels toward east at 100kmph
In 15 minutes it'll travel= \(\frac{15}{60}*100\)=25 KM
Truck travels towards north at 80kmph
in 20 minutes it'll cover=\(\frac{20}{60}*80\)=26.66 KM
the distance between the car at this point
\[D=\sqrt{25^2+26.66^2}\]
\[D=36.547 km\]

- anonymous

wait what formula did you use to find the distance?

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- anonymous

and the answer to this question is 21.1km :S in the answer key, idk how to get to the answer.

- ash2326

i used the square root of the two distances, I would have made a mistake somewhere if the answer is 21.1 KM

- ash2326

GT do you have any idea how we use the 48 degree here

- anonymous

I can try. I think your assumption that the "paths" form a Right Triangle seems to be the problem. My take is that, the car and truck are in this state:
|dw:1328462347280:dw|

- anonymous

You will need to use the sine rule of triangles to find the 3rd side I would imagine.

- ash2326

yeah i made that mistake we can use the cosine formula now , Thanks GT

- anonymous

cosine formula works and probably easier to plug away given the information.

- ash2326

\[D^2=25^2+26.6^2-25*26.6* cos 48\]

- anonymous

yeah, thank you :)

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