Problem 70 - Precalculus: A Concise Course

Question

Determine whether the statement is true or false. Justify your answer. N \(24^{\circ}\) E means 24 degrees north of east.

Step-by-Step Solution

Answer

The statement is False. The correct interpretation of N \(24^{\circ}\) E is 24 degrees East of North.

Step 1: Understanding Nautical Terms

To begin with, we need to understand what the term N \(24^{\circ}\) E means. The directions on a compass are traditionally divided into four cardinal directions: North (N), East (E), South (S) and West (W). The convention 'N \(24^{\circ}\) E' means starting from North, move 24 degrees towards the direction of East.

Step 2: Correct Understanding Statement

The given statement says, 'N \(24^{\circ}\) E means 24 degrees North of East.' However, this understanding is incorrect, our analysis from step 1 clearly states that the correct understanding should be 'N \(24^{\circ}\) E means 24 degrees East of North.'

Step 3: Concluding the Verdict

From the analysis of the term and the understanding of the statement given in the problem, it can be concluded that the given statement is false. The correct interpretation of N \(24^{\circ}\) E would be '24 degrees East of North instead of '24 degrees North of East'.

Key Concepts

Cardinal Directions

Cardinal directions are the four main points of a compass: North, East, South, and West. These are fundamental in navigating and describing locations or directions.

• North (N): This is the top point on a standard compass and is considered the primary cardinal direction.
• East (E): Located to the right when facing North, East is the direction from which the sun rises.
• South (S): Opposite to North, South is down on a compass or map.
• West (W): Located to the left when facing North, it is where the sun sets.

Understanding these directions is essential for interpreting any compass reading. By combining these cardinal points with degrees, precise directions can be obtained. For example, 'N 24° E' directs you to start from North and move 24 degrees towards East.

Compass Reading

Compass reading is about interpreting the direction indicated by the needle on a compass. Compasses point towards the magnetic north and are used to find directions based on cardinal points paired with degrees. When using a compass, always hold it flat in your hand and ensure it is stable.

The compass will point to magnetic north, and from there, you can determine other directions. To read a compass, you:

• Identify the cardinal direction where the needle points.
• Count the degrees from the starting cardinal point to your desired direction.
• Use the marked degrees on the compass to aid in this.

For example, N 24° E is read by identifying 24 degrees eastward from north. This helps in precise navigation.

Degrees Navigation

Degrees navigation refers to navigating using angles measured in degrees from a stated direction on a compass. A full circle is 360 degrees, and this system allows for a comprehensive and precise method of pointing out directions.

Degrees are crucial when you need to be more specific than the basic cardinal directions.

• 0°: Referencing directly North.
• 90°: Directly East.
• 180°: Directly South.
• 270°: Directly West.

Intermediate directions can be described by combining these cardinal points with specific degree measurements. For example, 'N 24° E' means from North, move 24 degrees towards East. It's essential to be clear about starting points and directions to avoid confusion, as seen in interpretations like '24 degrees North of East' versus '24 degrees East of North.' Properly understanding this ensures accurate navigation.