You are sailing from your lakeshore cabin to a marina 60º north of east and 0.5 miles across the lake. on your return trip, you decide to sail directly south and then west to get back to your cabin. how far would you now have to sail? a. 0.68 miles b. 0.43 miles c. 0.25 miles d. 0.5 miles

For this case what we should observe is that we have a rectangle triangle where we know:
 Angle.
 Hypotenuse.
 We want to know:
 opposite cateto
 Adjacent cateto
 We apply the following trigonometric formulas:
 Sine (x) = C.O / h
 Cosine (x) = C.A / h
 Where,
 x: angle
 C.O: opposite leg
 C.A: adjacent leg
 h: hypotenuse
 Substituting values:
 Sine (60) = C.O / 0.5
 Cosine (60) = C.A / 0.5
 Clearing:
 C.O = 0.5 * Sine (60) = 0.43
 C.A = 0.5 * Cosine (60) = 0.25
 Then, adding both sides we have:
 C.O + C.A = 0.43 + 0.25 = 0.68 miles
 
 you now woluld have to sail:
 a.
 0.68 miles