anonymous 4 years ago 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?

1. ash2326

See the picture

2. 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 $D=\sqrt{25^2+26.66^2}$ $D=36.547 km$

3. anonymous

wait what formula did you use to find the distance?

4. anonymous

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

5. ash2326

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

6. ash2326

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

7. 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|

8. anonymous

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

9. ash2326

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

10. anonymous

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

11. ash2326

$D^2=25^2+26.6^2-25*26.6* cos 48$

12. anonymous

yeah, thank you :)