Boat A is 20 km from port on a bearing of 025° and boat B is 25 km from port on a bearing of 070°. Boat B is in distress. What b
earing should boat A travel on to reach boat B?
1 answer:
Answer: Boat A should travel 152.8° to reach B
Step-by-step explanation:
The diagram illustrating the scenario is shown in the attached photo. Triangle ABP is formed. A represents the position of boat A. B represents the position of boat B. P represents the position of the port.
We would determine AB by applying the law of cosines
AB² = AP² + BP² - 2AP×BPCosP
AB² = 20² + 25² - 2 × 20 × 25 × Cos45
AB² = 1025 - 707.10678 = 317.89322
AB = √317.89322 = 17.83
We would determine the bearing of B from A by finding angle A. We would apply the sine rule.
AB/SinP = AP/Sin A
17.83/Sin45 = 20/SinA
Cross multiplying, it becomes
17.83 × SinA = 20Sin45 = 14.14
SinA = 14.14/17.83 = 0.79
A = Sin^-1(0.79) = 52.2°
The total angle at A is 65 + 52.2 = 117.2°
The angle formed outside the third quadrant is 117.2 - 90 = 27.2°
Therefore, bearing B from A is
180 - 27/2 = 152.8°
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