Solve the problem.
-Two ships leave a harbor together traveling on courses that have an angle of $123 ^ { \circ }$ between them. they each travel 506 miles, how far apart are they (to the nearest mile)?
A) $483 \mathrm { mi }$
B) $40 \mathrm { mi }$
C) $889 \mathrm { mi }$
D) $1778 \mathrm { mi }$

Question

Quizplus · Accepted Answer

To find the distance between the two ships after they have traveled, we can use the Law of Cosines since we have a non-right triangle formed by the paths of the two ships and the angle between them. The Law of Cosines is given by $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $a$ and $b$ are the sides of the triangle adjacent to angle $C$, and $c$ is the side opposite angle $C$. In this case, $a = 506$ miles, $b = 506$ miles, and $C = 123^\circ$.Plugging these values into the formula gives:$$c^2 = 506^2 + 506^2 - 2(506)(506)\cos(123^\circ)$$Using a calculator to find $\cos(123^\circ)$ and then solving for $c^2$, and finally taking the square root gives the distance $c$. After calculating, you find that $c \approx 889$ miles, which means the ships are approximately 889 miles apart, to the nearest mile.

Solve the Problem 123∘123 ^ { \circ }123∘ Between Them 483mi483 \mathrm { mi }483mi

Solve the Problem $123 ^ { \circ }$ Between Them $483 \mathrm { mi }$