You are sailing from your lakeshore cabin to a marina 60º north of east and 0.5 miles across the lake.Which of the following expressions uses the complementary angle of 60° to determine how far you would travel on your trip west?a.0.5cos30°b.0.5cos60°c.0.5sin30°d.0.5sin60°

Answer:- c. 0.5sin30°
Explanation:-Let AB= 0.5 miles be the distance across the lake to 60º north of east.AC= distance travel to the eastNow, in right ΔABC[tex]sin60^{\circ}=\frac{AC}{AB}\\\\\Rightarrow\ AB=ACsin60^{\circ}\\\Rightarrow\ AB=0.5\ sin60^{\circ}[/tex]Now Distance towards west  [tex]AD=|\ -0.5\ sin60^{\circ}|[/tex] [distance is a positive quantity][tex]AD=0.5\ sin60^{\circ}[/tex][tex]AD=0.5\ cos(90^{\circ}-60^{\circ})[/tex]  [Taking complementary angle of 60° ][tex]AD=0.5\ cos(30^{\circ})[/tex]Thus C. is the right option.