Question

Two ship ,P and X sailed from A at the same time .Ship P sails 21 nautical mile due east in 30 minutes and ship X sails 30 nautical miles in the same time on a bearing of 163° . How far are the ship apart?

Answer 1

To find the distance between the two ships, we can use trigonometry and the Law of Cosines.

First, we need to calculate the distance Ship X has traveled in the East direction and the North direction.

Distance traveled in the East direction by Ship X:
cos(163°) = adjacent / hypotenuse
cos(163°) = x / 30
x = 30 * cos(163°)
x ≈ -10.57 nautical miles (East direction)

Distance traveled in the North direction by Ship X:
sin(163°) = opposite / hypotenuse
sin(163°) = y / 30
y = 30 * sin(163°)
y ≈ 26.35 nautical miles (North direction)

Now, we need to find the distance between the two ships using the Law of Cosines:
c² = a² + b² - 2ab * cos(C)
c² = (21)² + (-10.57)² - 2 * 21 * (-10.57) * cos(90°)
c² = 441 + 111.72 + 445.14 * 0
c² = 552.72
c ≈ √552.72
c ≈ 23.51 nautical miles

Therefore, the two ships are approximately 23.51 nautical miles apart.