A cruise ship travels 310 miles due east before turning 20°
north of east. It travels 150 miles along its new course. How far is the cruise ship from its initial position?
454 miles
274 miles
160 miles
295 miles
To find the distance from the cruise ship's initial position, we need to use trigonometry.
First, we can find the distance traveled north by using the distance traveled along the new course and the angle 20°:
Distance north = 150 miles * sin(20°) = 150 miles * 0.342 = 51.3 miles
Next, we can find the distance traveled east by using the distance traveled along the new course and the angle 20°:
Distance east = 150 miles * cos(20°) = 150 miles * 0.940 = 141 miles
Now we can use the Pythagorean theorem to find the distance from the initial position:
Distance = sqrt((Distance east)^2 + (Distance north)^2)
Distance = sqrt((141)^2 + (51.3)^2)
Distance = sqrt(19881 + 2631)
Distance = sqrt(22512)
Distance ≈ 150.1 miles
So, the cruise ship is approximately 150.1 miles from its initial position.
Therefore, the closest answer option is 160 miles.