Question

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

Answer 1

b = 5 and c = 3

Explanation:

The law of cosines states:

b^2 = a^2 + c^2 - 2*a*c*cos(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 – 2*7*3*cos(B)

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

Answer 2

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