Question

For triangle ABC, a = 7.7 , b = 17.0 , c = 12.7. Find m∠C.

Answer 1

The triangle can be drawn as shown below:

The Cosine Rule can be applied in this case. It is given to be:

$\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ \cos C=\frac{a^2+b^2-c^2}{2ab} \end{gathered}$

From the question, we have the following measures:

$\begin{gathered} a=7.7 \\ b=17.0 \\ c=12.7 \end{gathered}$

Therefore, we can substitute and solve as shown below:

$\begin{gathered} \cos C=\frac{7.7^2+17.0^2-12.7^2}{2\times7.7\times17.0} \\ \cos C=\frac{187}{261.8} \\ \cos C=0.714 \end{gathered}$

Therefore, the measure of angle C will be gotten to be:

$\begin{gathered} C=\cos ^{-1}0.714 \\ m\angle C=44.4\degree \end{gathered}$

The measure of angle C is 44.4°.