Question 1168437: A ship travels on a N 28o E course. The ship travels until it is due north of a port which is 200 nm due east of the port from which the ship originated.
How far did the ship travel?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's solve this problem step-by-step.
**1. Visualize the Situation**
* Draw a horizontal line representing the east-west direction.
* Let P1 be the port from which the ship originated.
* Let P2 be the port due north of P1's final position.
* P2 is 200 nautical miles (nm) east of P1.
* The ship travels on a N 28° E course. This means it travels at an angle of 28° from the north direction towards the east.
**2. Set Up the Triangle**
* The ship travels from P1 to a point S.
* S is due north of P2.
* We have a right triangle P1SP2.
* P1P2 = 200 nm (eastward distance)
* Angle SP1P2 = 90° - 28° = 62°
**3. Use Trigonometry**
We need to find the distance P1S, which is the distance the ship traveled.
* We have angle SP1P2 = 62°, and we know the adjacent side (P1P2 = 200 nm).
* We need to find the hypotenuse (P1S).
* We can use the cosine function:
cos(angle) = adjacent / hypotenuse
* cos(62°) = P1P2 / P1S
* cos(62°) = 200 / P1S
**4. Solve for P1S**
* P1S = 200 / cos(62°)
* cos(62°) ≈ 0.4695
* P1S = 200 / 0.4695
* P1S ≈ 425.98 nm
**5. Round to an Appropriate Number of Decimal Places**
We can round to two decimal places, as it's a practical distance measurement.
P1S ≈ 426.00 nm
**Therefore, the ship traveled approximately 426.00 nautical miles.**
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