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=(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=(7.7^2+17.0^2-12.7^2)/(2*7.7*17.0) \\ \cos C=(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°.