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.

A right triangle. The hypotenuse is 0.5, and an angle is 60 degrees.
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

Since you sailed 0.5 miles 60º north of east to reach the marina, the distance you sailed eastward is 0.5cos(60º) = 0.25 miles and the distance you sailed northward is 0.5sin(60º) = 0.433 miles.

To return to your cabin, you sailed directly south for 0.433 miles, forming the adjacent side of a right triangle, and then sailed directly west for 0.25 miles, forming the opposite side of the same right triangle.

Therefore, the distance you sailed on your return trip is the hypotenuse of the right triangle, which can be found using the Pythagorean theorem:

distance = sqrt((0.433)^2 + (0.25)^2) ≈ 0.51 miles

Rounded to the nearest hundredth, the distance you sailed on your return trip is 0.51 miles, which is closest to option (a) 0.68 miles.