Question

Consider the triangle shown below where m∠B=78∘, a=35.9 cm, and c=31.2 cm.Use the Law of Cosines to determine the value of x (the length of ACin cm).x=

Answer 1

Applying the law of cosines we have

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

substitute the given values

`\begin{gathered} x^2=35.9^2+31.2^2-2(35.9)(31.2)\cos (78^o) \\ x^2=1,796.49 \\ x=42.4\text{ cm} \end{gathered}`