Question 598015: Two factories blow their whistles at exactly the same time. If a man hears the two blasts exactly 2.5 seconds and 5.1 seconds after they are blown and the angle between his lines of sight to the two factories is 28.4 degrees, how far apart are the factories? Give your result to the nearest meter. ( use the fact that sound travels at 344 m/sec).
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two factories blow their whistles at exactly the same time.
If a man hears the two blasts exactly 2.5 seconds and 5.1 seconds after they are blown
and the angle between his lines of sight to the two factories is 28.4 degrees,
how far apart are the factories?
Give your result to the nearest meter. ( use the fact that sound travels at 344 m/sec).
:
Find the distances between the man and the factories
5.1 * 344 = 1754.4 m
2.5 * 344 = 860 m
:
The side opposite the angle of 28.4 degrees will be the distance between the factories.
A "side/angle/side" problem.
:
We can use the law of cosines
a^2 = b^2 + c^2 - 2bc*cos(A), where
a = distance between the factories
b = 1754.4
c = 860
A = 28.4 degrees
:
a^2 = 1754^2 + 860^2 - 2(1754.4*860)*cos(28.4)
After some tedious math, I got 1078.48 meter between the factories
See what you get.
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