Final answer:
To find the distance from point c to port b, we construct a right-angled triangle and use trigonometry to calculate the northward displacement before applying the Pythagorean theorem.
Step-by-step explanation:
The student's question involves calculating the distance of a yachtsman from port b after sailing from port a to a point c on a certain bearing. Since the yachtsman sails 8 km on a bearing of 070°, this forms the first side of a right-angled triangle with the eastward displacement of 9 km forming the second side. To find the distance he is from port b, we must calculate the northward distance he has now covered and then use the Pythagorean theorem to find the hypotenuse of the triangle, which is the required distance from point c to port b.
By drawing the scenario, we can see that we have a right-angled triangle where the horizontal leg represents the 9 km distance from a to b, and the 8 km distance from a to c forms the hypotenuse. Using trigonometry, the northward displacement (vertical leg) can be found, and subsequently the distance from c to b can be calculated.