Question

Which equation could be used to solve for the length of side c, given a = 5, b = 12, and c = 72°?

Answer 1

c^2=a^2+b^2-2abcos(c)
c=sqrt(a^2+b^2-2abcos(c))
c=sqrt((5)^2+(12)^2-2(5)(12)cos(72))
c=sqrt(25+144-120cos(72))
c=sqrt(169-120cos(72))
c=sqrt(169-37.08)
c=sqrt(131.92)
c=11.49

Answer 2

`c=11.49`

Explanation:

It is given that a = 5, b = 12, and c = 72°, then using the cosine formula, we get

`c^2=a^2+b^2-2abcosC`

`c^2=(5)^2+(12)^2-2(5)(12)Cos72^(\circ)`

`c^2=25+144-2(60)(0.309)`

`c^2=169-37.08`

`c^2=131.92`

`c=√(131.92)`

`c=11.49`

Therefore, the value of the length of the side c is 11.49.