Answer in Trigonometry
A ship sails from port P on course N 300 E. After sailing 3 miles it changes course 3000 true and sailed 4 miles. How far is the ship at the lighthouse?
The diagram shows the starting point of the ship from point P on a bearing of N30°E at distance 3 miles and then changed direction on the bearing 300° at distance 4 miles.
We are then to find the distance of the final point from the starting point.
From the diagram, the angle subtended by the 3miles and 4 miles directions is 90° and the unknown distance is denoted x miles.
So, by the cosine rule
x2 = a2 + b2 – 2abcosθ
where a=3, b=4 and θ=90°
x2 = 32 + 42 – 2(3)(4)cos(90°)
x2 = 9 + 16 – 24(0), since cos(90°)=0
x2 = 25
Finding the square root of both sides
Hence, the distance of the ship at the lighthouse is 5 miles.
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