Answer:
The distance covered by boat is 18.44 miles.
Step-by-step explanation:
Use the given information to draw a figure.
[tex]\angle B=\angle BCN=40^{\circ}[/tex] (Alternate interior angles)
[tex]\angle BCN+\angle BCA+\angle ACS=180^{\circ}[/tex] (Supplementary angles)
[tex]40^{\circ}+\angle BCA+40^{\circ}=180^{\circ}[/tex]
[tex]\angle BCA=100^{\circ}[/tex]
According to angle sum property of a triangle, the sum of interior angles is 180 degree.
[tex]\angle A+\angle B+\angle BCA=180^{\circ}[/tex]
[tex]40^{\circ}+\angle B+100^{\circ}=180^{\circ}[/tex]
[tex]\angle B=40^{\circ}[/tex]
Since two angles are same, therefore ABC is isosceles triangle.
[tex]BC=AC[/tex]
Use Law of Sine:
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
[tex]\frac{BC}{\sin A}=\frac{AC}{\sin C}[/tex]
[tex]\frac{BC}{\sin 40}=\frac{8}{\sin 100}[/tex]
[tex]BC=\frac{8}{\sin 100}\times \sin 40=5.22[/tex]
[tex]BC=AC=5.22[/tex]
The perimeter of triangle ABC is
[tex]AB+BC+CA=8+5.22+5.22=18.44[/tex]
Therefore the distance covered by boat is 18.44 miles.
