Solve the problem.
-Island A is 150 miles from island B. A ship captain travels 250 miles from island A and then finds that he is off course and 160 miles from island B. What angle, in degrees, must he turn through to head straight for island B?
Round the answer to two decimal places. (Hint: Be careful to properly identify which angle is the turning
Angle.)
A) $145.08 ^ { \circ }$
B) $110.17 ^ { \circ }$
C) $55.08 ^ { \circ }$
D) $34.92 ^ { \circ }$

Question

Solve the problem.
-Island A is 150 miles from island B. A ship captain travels 250 miles from island A and then finds that he is off course and 160 miles from island B. What angle, in degrees, must he turn through to head straight for island B?
Round the answer to two decimal places. (Hint: Be careful to properly identify which angle is the turning
Angle.) 
A) $145.08 ^ { \circ }$
B) $110.17 ^ { \circ }$
C) $55.08 ^ { \circ }$
D) $34.92 ^ { \circ }$

Quizplus · Accepted Answer

The problem can be solved using the Law of Cosines. Given the sides of the triangle formed by the distances (150 miles, 250 miles, and 160 miles), the angle opposite the 250-mile side can be found. Let $c = 250$ miles, $a = 150$ miles, and $b = 160$ miles. The Law of Cosines formula is $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $C$ is the angle opposite side $c$. Solving for $\cos(C)$ gives the angle $C$, which is the deviation from the original course. The calculation yields an angle of approximately $145.08^\circ$, indicating the captain must turn through this angle to head straight for island B.

Solve the Problem 145.08∘145.08 ^ { \circ }145.08∘ B) 110.17∘110.17 ^ { \circ }110.17∘

Solve the Problem $145.08 ^ { \circ }$ B) $110.17 ^ { \circ }$