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A ship is sailing on a bearing of 215°from port until it is 100km due to south of port. How far does it sail to the nearest km

215 - 180 = 35 deg west of south

so south distance = d cos 35
so
d = 100 / cos 35

By the way you TAKE a bearing. You sail on a HEADING. Clue your textbook in.

Did you know?

Did you know that the distance a ship sails to the nearest kilometer can be determined using basic trigonometry and navigation principles? In the given scenario, a ship sails on a bearing of 215° from the port until it reaches a point 100 km directly south of the port. By visualizing the situation on a coordinate plane, we can determine that the ship has formed a right-angled triangle. The bearing angle of 215° provides the opposite side of the triangle (100 km) and the hypotenuse (the distance sailed) can be found using the sine function. Applying the sine function, we find that sin(215°) ≈ 0.727, which means the distance sailed is approximately 100 km ÷ 0.727 ≈ 137.61 km. Rounding to the nearest kilometer, the ship sails approximately 138 km.