Answer:
B.18. 44 miles
Step-by-step explanation:
We are given that
Distance between A and B=8 miles
Angle B=Angle BCQ=40 degree (Alternate interior angles)
Angle ACB=180-Angle ACP-Angle BCQ
Angle ACB=180-40-40=100 degree
In triangle ABC
Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property
Substitute the values
[tex]\angle A+40+100=180[/tex]
[tex]\angle A+140=180[/tex]
[tex]\angle A=180-140[/tex]
[tex]\angle A=40[/tex] degree
Angle A=Angle B
When two angles are equal of a triangle then the triangle is isosceles triangle.
Therefore, triangle ABC is an isosceles triangle.
[tex]\implies BC=AC [/tex]
Now, Sine law
[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Using the sine law
[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]
[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]
[tex]BC=\frac{8\times sin40}{sin 100}[/tex]
BC=5.22
AC=BC=5.22 miles
Now, total distance covered by the boat=AB+BC+AC
Total distance covered by the boat=8+5.22+5.22=18.44 miles
Hence, option B is correct.
