Question

using the law of cosines given sss information
find the measure of \\( \angle a \\) in \\( \triangle abc \\).
since we are given sss information here, we can use the following equation to solve for \\( m\angle a \\).
complete
\\( 55^{2}=50^{2}+35^{2}-2(50)(35)\cos(a) \\)
after working through the problem above, we get \\( \cos(a)= \\)

Explanation:

Step1: Expand the squares

$$\begin{align*} 55^{2}&=50^{2}+35^{2}-2(50)(35)\cos(A)\\ 3025&=2500 + 1225-3500\cos(A) \end{align*}$$

Step2: Simplify the right - hand side

$$\begin{align*} 3025&=3725-3500\cos(A) \end{align*}$$

Step3: Isolate the term with \(\cos(A)\)

$$\begin{align*} 3500\cos(A)&=3725 - 3025\\ 3500\cos(A)&=700 \end{align*}$$

Step4: Solve for \(\cos(A)\)

$$\begin{align*} \cos(A)&=\frac{700}{3500}\\ \cos(A)& = 0.2 \end{align*}$$

Answer:

\(0.2\)