Question 341387: Which triangle should be solved by beginning with the Law of Cosines?
a. A = 115 degrees, a = 19, b = 13
d. A = 62 degrees, B = 15 degrees, b = 10
c. B = 48 degrees, a = 22, b = 5
d. A = 50 degrees, b = 20, c = 18
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The law of cosines states that:
c^2 = a^2 + b^2 - 2abCos(C)
or:
a^2 = b^2 + c^2 - 2bcCos(A)
or:
b^2 = a^2 + c^2 - 2acCos(B).
You know the value of 2 sides and the included angle between them.
If you draw a triangle ABC, then side AB is equal to c, side BC is equal to a, and side AC is equal to b.
a is opposite angle A.
b is opposite angle B.
c is opposite angle C.
If a is opposite angle A, then angle A has to be included between sides b and c.
If b is opposite angle B, then angle B has to be included between sides a and c
If c is opposite angle C, then angle C has to be included between sides a and b.
It looks like option D is your choice.
That states that:
A = 50 degrees, b = 20, c = 18
Side a is opposite angle a which means that angle A is included between sides b and c.
Your law of cosines formula would be:
a^2 = b^2 + c^2 - 2bcCos(A).
Draw yourself triangle ABC.
Side a is opposite angle A.
Side b is opposite angle B.
Side c is opposite angle C.
You can see that side a is the unknown sides and that angle A is between the known sides of b and c.
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