Answer to Question #245290 in Trigonometry for John lee Monton

Question

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?

Answer 1

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

x= 5

Hence, the distance of the ship at the lighthouse is 5 miles.