CHECK THE COMPLETE QUESTION BELOW
Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160 miles from island B. What bearing should he turn to, so he is heading straight towards island B?
A. 111.65
B. 119.84
C. 21.65
D. 135.53
Answer:
OPTION A IS CORRECT
A. 111.65
Step-by-step explanation:
This question can be explained using a triangle, let us say triangle ABD
and let us say A and B represent the islands and D is the particular point from where the captain is standing at a distance of 160 miles from B island .
We will be making use of cosines rule to calculate our angles, and we know that from cosine rule
D² = a² + b² -2abCosD
Where, a= 160 b = 260 and d = 250 then we can substitute in order to calculate our angles
250²= 60² + 260² - 2(160*260)Cos(D)
62500= 625600+ 67600- 83200CosD
83200CosD= 25600+ 67600 - 625600
83200CosD= 30700
CosD= 30700/83200
CosD= 0.369
D= cos⁻¹ (0.369)
D=68.35
Therefore, the angle inside the triangle is 68.35°
Now we can now find the bearing the captain supposed to turn , if he is heading to island B which will be the external angle of the triangle, but we know that The external angle =180°(supplimentary angles )
Then the angle he would turn will be external angle of the triangle - 68.35°
= (180 - 68.35)
= 111.65°
Therefore, the bearing the captain should turn is 111.65° for him to be heading straight towards island B.
