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The bearing from city A to city B

The bearing from city A to city B is S 40 degrees E and the bearing from city B to city C is N 25 degrees E. It takes 2.1 hours for a car traveling at 54 miles per hour to go from A to B and 1 hours to go from B to C.
Find the distance between city A and city C.

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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
5.0 5.0 (3 lesson ratings) (3)
In this problem, you are supposed to use the Law of Cosines, a generalization of the Pythagorean theorem. Pythagorean gives you the third side of a right triangle; the Law of Cosines does the same for any triangle, if you know the angles. It states
c2 = a2 + b2 -2ab cos θ,
where θ is the angle between sides a and b. Notice that if θ=90°, cos θ=0, and you get back the Pythagorean theorem.
In this problem, the three sides of the triangle are the distances between A and B (=a), B and C (=b), and C and A (=c, unknown). We have a= 54*2.1=113.4 miles and b = 54*1=54 miles. The angle between cities A and C, as measured at B, is θ=180-40-25=115°. Therefore,
c2= 113.42+542-2(113.4)(54)cos(115) = 20951,
c = 145 miles.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
Hi Dalia;
distance=[(54 miles/hour)(2.1 hours)]+[(54 miles/hour)(1 hour)]
Let's cancel units...
Hours is in both the numerators and denominators of both bracketed equations...
distance=[(54 miles/hour)(2.1 hours)]+[(54 miles/hour)(1 hour)]
distance=[(54 miles)(2.1)]+[(54 miles)(1)]
The only units remaining are miles, which is what we want...
distance=(113.4+54) miles
distance=167.4 miles
I do not know why the bearings are provided.


This is not correct at all. This is a trigonometry problem applying the Law of Cosines, not a basic algebra problem using d=(r)(t) should take this down..and re-think if teaching is a good option for you...