To find the distance the cruise ship is from its initial position, we can use the Law of Cosines.
Let's call the distance from the end of the 150-mile segment to the initial position of the cruise ship (x) and the angle between the 310-mile segment and x (160 degrees, since the angle north of east is 20 degrees).
Using the Law of Cosines:
x^2 = 310^2 + 150^2 - 2(310)(150)cos(160)
x^2 = 96100 + 22500 - 93000cos(160)
x^2 = 118600 - 93000cos(160)
x^2 ≈ 118600 - 93000(-0.9397)
x^2 ≈ 118600 + 87473.1
x^2 ≈ 205073.1
x ≈ √205073.1
x ≈ 453.4
So, the cruise ship is approximately 453.4 miles from its initial position.
The closest option provided is 454 miles.
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?
A triangle is shown. Its horizontal base is labeled 310 miles, and at the right end of the line segment, the line extends with a dashed line. From the right endpoint of the 310-mile segment, another segment and side of the triangle extends up and to the right, and it’s labeled 150 miles. The angle formed between the 150-mile line segment and the extended dashed horizontal line is labeled 20 degrees. A line is drawn that connects the far endpoints of the 310-mile and the 150-mile segments and completes the triangle. It is labeled x.
(1 point)
Responses
295 miles
295 miles
274 miles
274 miles
454 miles
454 miles
160 miles
1 answer
1 answer