To solve this question, use the law of cosines shown below:
[tex]c^2=a^2+b^2-2*a*b*cosC[/tex]
In this question,
a = 6
b = 8
C = 10°
First, let's find c:
[tex]\begin{gathered} c^2=6^2+8^2-2*6*8*cos10 \\ c^2=36+64-94.54 \\ c^2=5.46 \\ \sqrt{c^2}=\sqrt{5.456} \\ c=2.34 \end{gathered}[/tex]
Second, let's find A.
Now, a, b, and c are known, and Cos A is not known:
[tex]\begin{gathered} a^2=b^2+c^2-2bc*cosA \\ 6^2=8^2+2.34^2-2*8*2.34*cosA \\ 36=64+5.48-37.44*cosA \\ 36=69.48-37.44*cosA \\ \text{ Subtracting 69.46 from both sides:} \\ 36-69.48=69.46-37.44*cosA-69.46 \\ -33.48=-37.44*cosA \\ \text{ Dividing both sides by -37.44:} \\ \frac{-33.48}{-37.44}=\frac{-37.44}{-37.44}cosA \\ 0.8942=cosA \\ Then, \\ A=cos^{-1}(0.8942) \\ A=26.6 \end{gathered}[/tex]
Answer:
c = 2.34 units
A = 26.6°
