## anonymous 4 years ago Two cars leave from the same point (A) and travel along a straight road, which are at angle of 78° to each other. If their speeds are 120 km/h (truck) and 90 km/h (car) respectively, how far apart will they be after one half hour? a. Draw a diagram. b. Distance = speed x time

1. anonymous

Distance traveled by car 1 = 60 Distance traveled by car 2 = 45 Now, we can use the rule of cosines, $$\sqrt{60^2 +45^2- 2\times\cos 78^\circ\times60 \times 45 } = \cdots$$

2. anonymous

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3. anonymous

How did you get the distance? Since you both have different answers?

4. anonymous

Law of cosines:$c ^{2} = a ^{2} + b ^{2} - 2abcos(\gamma)$ So: sqrt(60^2 + 30^2 - 2*30*60*cos(78)) = ~61

5. anonymous

why 30 lauriy? Am I missing something ...

6. anonymous

Sorry not 30 but 45... sqrt(60^2 + 45^2 - 2*45*60*cos(78)) = ~67.1

7. anonymous

Uhm- I still don't understand how the distance go calculated? Like, how did you get 60, and 45? what steps? I understand the cos law, Thanks

8. anonymous

120km/h means 120 in 1 hour. So if he only has half an hour, he will do 60 km.

9. anonymous

Oh wow! LOL, that makes sense! Thanks a bunch!