Bearing Problems & Navigation

Summary

This video explains the concept of bearings, focusing on how to draw and calculate them using angles measured relative to the north-south line. It demonstrates various examples, including bearings like 'north 30 degrees east' and 'south 50 degrees west,' and explores how to determine distances and directions in real-world scenarios. The script also delves into trigonometric functions like sine and cosine for calculating distances traveled in specific directions. Word problems are presented to show practical applications, including how to find bearings and distances in navigation, such as for cars, boats, and people.

Takeaways

• 😀 Bearings are angles measured relative to the north-south line, starting from either north or south and moving towards east or west.
• 😀 A bearing of 'north 30 degrees east' means starting from the north line and moving 30 degrees towards the east.
• 😀 A bearing of 'north 20 degrees west' means starting from the north line and moving 20 degrees towards the west.
• 😀 Bearings are typically represented by two components: the first letter is either 'N' or 'S', and the second is either 'E' or 'W'.
• 😀 When given an angle, use the angle between the direction line and the north-south line to determine the correct bearing.
• 😀 To calculate bearings accurately, always measure angles starting from the correct reference line (north or south).
• 😀 If an angle is provided with respect to the east or west line, adjust the angle by subtracting it from 90° to get the correct bearing.
• 😀 Trigonometric functions like sine and cosine are used to find distances and bearings in word problems involving movement along a bearing.
• 😀 In word problems, when traveling at a specific bearing, break the journey into components using trigonometric functions to calculate north/south and east/west distances.
• 😀 For right-angle triangles, the Pythagorean theorem is useful to find distances (hypotenuse), and the tangent function helps find angles in the triangle.
• 😀 Bearings can also be used to find the distance between two points, such as calculating how far an object is from a given reference point based on given directions and distances.

Q & A

What does the bearing 'north 30 degrees east' represent?

The bearing 'north 30 degrees east' means starting from the north line and traveling 30 degrees toward the east. It represents the direction in which an object is moving relative to the north-south line.

How do you draw a bearing of 'north 20 degrees west'?

To draw 'north 20 degrees west,' start with the north-south line, then travel 20 degrees toward the west from the north line. The bearing is represented by a line in this direction.

Why are bearings always measured relative to the north-south line?

Bearings are always measured relative to the north-south line because it provides a consistent reference point for direction. This helps standardize how angles are described, regardless of whether the direction is east, west, north, or south.

What is the bearing if an object is moving in the direction of a line with a 40-degree angle from the north-south line?

If an object is moving in the direction of a line with a 40-degree angle from the north-south line, the bearing should be 'south 40 degrees east,' because we measure from the south line and travel towards the east.

How do you handle an angle of 20 degrees relative to the east line when calculating bearings?

When given an angle of 20 degrees relative to the east line, the angle you need to use is 70 degrees, as bearings are measured from the north-south line. To find this, subtract 20 from 90 degrees (since the angle between the north-south line and the east line is 90 degrees).

What is the correct bearing for an object moving at an angle of 60 degrees relative to the south line?

The correct bearing for an object moving at an angle of 60 degrees relative to the south line is 'south 60 degrees west.' This is because the angle is measured from the south line, traveling towards the west.

How do you calculate the north and east distances when a car travels at a bearing of 'north 40 degrees east' for 300 miles?

To calculate the north and east distances, use trigonometric functions. For the north distance, use the sine function: 300 * sin(50 degrees), which gives about 229.8 miles. For the east distance, use the cosine function: 300 * cos(50 degrees), which gives about 192.8 miles.

What bearing should a boat take if it is 12 miles west and 15 miles south of an island?

The boat should take a bearing of 'north 38.7 degrees east' to travel directly to the island. This is calculated by first determining the angle between the boat and the island using the tangent function, and then finding the bearing relative to the north line.

How do you calculate the distance between John and the crocodile, based on their positions?

To calculate the distance, use trigonometry. Given that John is north of the crocodile, and Susan is 500 feet east of John, we use the tangent of the angle between Susan's line of sight and the north-south line to find the distance. The result is that John is approximately 800 feet from the crocodile.

If a boat travels 36 miles at a bearing of north 53 degrees east and then makes a 90-degree clockwise turn to travel 15 miles on a bearing of south 37 degrees east, how far is the boat from the island?

To find the distance from the island, use the Pythagorean theorem. The boat’s total displacement forms a right triangle, with one side measuring 36 miles and the other 15 miles. The hypotenuse of the triangle is the distance from the island, which is approximately 39 miles.