Respuesta :
The ship captain should be turned 129.49 so it's heading straight for Island B.
Given Island A is 160 miles from Island B and the captain of a ship travels 170 miles from Island A and then discovers that he is off course and 200 miles from island B.
So we gave it
a = 200 feet
b = 170 feet
c = 160 feet
We need to find angle C which goes directly to island B.
We apply the "cosine law":
[tex]\begin{aligned}\cos C&=\frac{a^2+b^2-c^2}{2ab}\\ &=\frac{(200)^2+(170)^2-(160)^2}{2\times 200\times 170}\\ &=\frac{40000+28900-25600}{68000}\\ &=\frac{43300}{68000}\\ &=0.636\end[/tex]
Now we multiply both sides by cos⁻¹, we get
cos⁻¹(cos C)= cos⁻¹(0.636)
C = 50.51
The interior angle is 50.51°
We need to find the outer angle to find the bearing the captain needs to turn
Applying the additional angle ruler:
The outside angle = 180 - 50.51 = 129.49°
Therefore, he must turn so as to head directly for Island B, where Island A is 160 miles from Island B and the captain is sailing 170 miles.
from Island A and then discovers that it is off-road and 200 miles away
Island B is 129.49.
Learn more about cosine law from here brainly.com/question/12902173
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