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two cars start moving from same location.head straight.but different directions. The...

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r4rob92 | (Level 1) Valedictorian

Posted May 13, 2013 at 5:18 PM via web

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two cars start moving from same location.head straight.but different directions.

The angle between where they are heading is 43degrees.The first car travels 20 miles and the second 37 miles.How far apart are the cars

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mvcdc | Student, Graduate | (Level 1) Associate Educator

Posted May 13, 2013 at 5:37 PM (Answer #1)

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This is an application of the Law of Cosine:

`c^2 = a^2 + b^2 - 2abcosC`

C here is the given angle and c (smaller) is the length of the side opposite to angle C; a and b are the other two legs. Hence, to solve for the distance of the two cars, we simply solve for c:

`c^2 = 20^2 + 37^2 - 2(20)(37)cos(43) = 400 + 1369 - 1480*0.73 = 688.6.`

Taking square roots, we see that c = 26.24 miles.

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