In a triangle \(\mathrm{ABC}, \mathrm{a}=5 \mathrm{~cm}, \mathrm{~b}=7 \mathrm{~cm}\) and angle \(\mathrm{C}=60^{\circ}\). Find \(\mathrm{c}\)
A. \(2 \mathrm{~cm}\) B. \(\sqrt{119 \mathrm{~cm}}\) C. \(\sqrt{39 \mathrm{~cm}}\) D. \(6 \mathrm{~cm}\)
Correct Answer: C
Explanation
To find \(c\), use is made of cosine rule (see) \(\Rightarrow \mathrm{c}^2=\mathrm{a}^2+\mathrm{b}^2-2 \mathrm{abcos} \mathrm{C}\) \begin{array}{l} \Rightarrow c^2=a^2+b^2-2 a b c o s c \\ c^2+5^2-25+49-70 \times 1 / 2 \\ c=\sqrt{39} c m \end{array}
