Question

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

Answer 1

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
Answer:
you now woluld have to sail:
a.
0.68 miles