goblinqueen
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The law of cosines for ABC can be set up as 52 = 72 + 32 – 2(7)(3)cos(B). What could be true about ABC? Law of cosines: a2 = b2 + c2 – 2bccos(A) a = 5 and c = 7 a = 3 and c = 3 b = 7 and c = 5 b = 5 and c = 3

Verified Answer :

A)a = 5 and c = 7

B) a = 3 and c = 3

C) b = 7 and c = 5

D) b = 5 and c = 3

Answer : b = 5 and c = 3

\(5^2 = 7^2 + 3^2 - 2(7)(3)cos(B)\)

The  cosine formula is

\(a^2 = b^2 + c^2 - 2bccos(A)\)

Given equation has cos(B) so we put b^2 before the = sign

So the formula becomes  

\(b^2 = a^2 + c^2 - 2accos(B)\)

Compare the given equation with the above cosine formula

\(5^2 = 7^2 + 3^2 - 2(7)(3)cos(B)\)

The value of b = 5, a= 7  and c=3

So, b = 5 and c = 3

Answer:

b = 5 and c = 3

Step-by-step explanation:

The law of cosines states:  

b^2 = a^2 + c^2 - 2accos(B)

where B is the angle opposite to side b, and a and c are the other two sides of the triangle.

From data we know that

5^2 = 7^2 + 3^2 – 273cos(B)

So, a = 7, c = 3 and b = 5

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