Question

In a triangle with sides a, b, c and angles A, B, C, the Law of Cosines states that ____.

Short answer

In a triangle with sides a, b, c and angles A, B, C, the Law of Cosines states that,

$$\begin{gathered} a^2=b^2+c^2-2bc\times \cos A \\ {b}^2=a^2+c^2-2ac\times \cos B \\ {c}^2=a^2+b^2-2ab\cos C \end{gathered}$$.

Step-by-step solution

Step 1. Given Information 

We are given a triangle with sides a, b, c and angles A, B, C.

We have to fill in the blanks.

Step 2. Completing the statement

The law of cosine will be,

$$\begin{gathered} a^2=b^2+c^2-2bc\times \cos A \\ {b}^2=a^2+c^2-2ac\times \cos B \\ {c}^2=a^2+b^2-2ab\cos C \end{gathered}$$

Hence the given statement can be completed as,

In a triangle with sides a, b, c and angles A, B, C, the Law of Cosines states that,

$$\begin{gathered} a^2=b^2+c^2-2bc\times \cos A \\ {b}^2=a^2+c^2-2ac\times \cos B \\ {c}^2=a^2+b^2-2ab\cos C \end{gathered}$$