Follow the questions given in the exercise. Use the Law of Sines.
97.4 mi
Practice makes perfect
Since there is a lot of information given, let's organize it in one graph to have a better understanding of the situation.
The distance that we are asked to find is represented by x. In order to find this distance we would like to form an equation using the Law of Sines.
However, we need two ratios between sine values of angles and the lengths of their opposite sides.
sin 22/x=sin □/□We need to find a second pair to create a ratio. The second angle we are given, 30^(∘), is an exterior angle. To find the measure of an interior angle, notice that the interior and exterior angles of any polygon form a linear pair. This means that their measures add to 180. Let's call the interior angle θ.
30+θ=180 ⇔ θ=150
The measure of the interior angle is 150. Now, we need to find the length of a side opposite to this angle.
This distance is a difference between the length of the original flight and the distance until the plane changed its course.
210-80=130
Now that we have the distance and the interior angle we can complete the previous equation.
sin 22/x=sin 150/130
Let's solve the equation for x.
