Question

You are on a fishing boat that leaves it's pier and heads east. After traveling for 30 miles there is a report warning of rough seas directly south. The captain turns the boat and follows a bearing of south 45 degrees west for 12 miles. At this time how far are you from the boats pier?

Answer 1

To find out how far the fishing boat is from the pier after traveling on a given path, represent the journey as a right-angled triangle and apply the Pythagorean theorem considering the boat's travels east and south-west.

Step-by-step explanation:

The question asks to determine how far the fishing boat is from the pier after it has traveled 30 miles east and then turns to follow a bearing of south 45 degrees west for 12 miles. This is a problem involving vector addition and Pythagorean theorem in mathematics, specifically within the topic of trigonometry. To solve this, we can represent the boat's journey as a right-angled triangle, with the first leg being 30 miles to the east, and the second leg being 12 miles on a bearing of south 45 degrees west.

Because the bearing is 45 degrees, the path south 45 degrees west will form a right-angle triangle with equal legs; that means the boat would travel an equal distance south and west which is 12 miles divided by the square root of 2, or approximately 8.49 miles in both the south and west directions from the point it turned. To find the distance from the pier, we apply the Pythagorean theorem: √((30 - 8.49)^2 + (8.49)^2).