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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)
1
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)
-2
Hi Dalia;
 
distance=[(rate)(time)]+[(rate)(time)]
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.

Comments

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)..you should take this down..and re-think if teaching is a good option for you...