Question

TRIGONOMETRY How far is the motorcycle from it’s starting point? Round to the nearest tenth

Answer 1

The above diagram illustrates the situation. We need to find side c of the triangle.

The measure of angle C is:

`\begin{gathered} 52\degree+m\angle C=180\degree \\ m\angle C=180\degree-52\degree \\ m\angle C=128\degree \end{gathered}`

Applying the law of cosines, the length of side c is:

`\begin{gathered} c^2=a^2+b^2-2ab\cos (m\angle C) \\ \text{ Substituting with data:} \\ c^2=20^2+38^2-2\cdot20\cdot28\cdot\cos (128\degree) \\ c^2=400+1444+2\cdot20\cdot28\cdot0.615 \\ c=\sqrt[]{2532.8} \\ c=50.3\text{ miles} \end{gathered}`