To find the distance between ship P and ship X, we first need to find the coordinates of their positions.
For ship P:
Distance sailed = 21 nautical miles
Time taken = 30 minutes = 0.5 hours
Speed of ship P = Distance / Time = 21 / 0.5 = 42 nautical miles per hour
Ship P sails due East, so its position is (21, 0)
For ship X:
Distance sailed = 30 nautical miles
Time taken = 30 minutes = 0.5 hours
Speed of ship X = Distance / Time = 30 / 0.5 = 60 nautical miles per hour
Ship X sails on a bearing of 136°, so its position can be calculated using trigonometry.
Using trigonometry:
x = 30 * cos(136°) ≈ -14.03 nautical miles
y = 30 * sin(136°) ≈ 24.11 nautical miles
So, the position of ship X is (-14.03, 24.11)
Now, we can find the distance between the two ships using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((-14.03 - 21)^2 + (24.11 - 0)^2)
Distance = sqrt((-35.03)^2 + 24.11^2)
Distance = sqrt(1226.5009 + 581.2921)
Distance = sqrt(1807.793)
Distance ≈ 42.52 nautical miles
Therefore, the two ships are approximately 42.52 nautical miles apart.