Problem 74 - Precalculus Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The bearing from \(O\) to \(B\) is \(E 70^{\circ} \mathrm{S}\)

Step-by-Step Solution

Answer

The statement makes sense. It denotes a location 70 degrees towards the east from the south of point O.

Step 1: Understanding the Bearing Notation

A bearing is a way of indicating the direction between two points in a clockwise direction. The notation 'E 70 S' would denote 70 degrees east from the south.

Step 2: Visual Representation

Draw a compass, place point O at the center. The southern direction is the starting point, from there move 70 degrees towards the east, that's where point B would be.

Step 3: Analyzing the Statement

Given the explanation and visual representation from previous steps, the statement 'The bearing from O to B is E 70 S' makes sense.

Key Concepts

Understanding Compass Directions

When it comes to navigating our world, compass directions are fundamental. They help us pinpoint locations and provide paths for travel. Imagine a circle divided into four main parts: North (N), South (S), East (E), and West (W). These are called the cardinal directions, and they are separated by 90 degrees.

Intercardinal directions further break these main divisions down. For example, Northeast (NE) lies between North and East, splitting the 90-degree angle into two 45-degree segments. This pattern is repeated around the compass: Southeast (SE) between South and East, Southwest (SW) between South and West, and Northwest (NW) between North and West.

Navigating often involves more than just these eight directions, which is where bearing measurements come into play. Instead of stopping with North, South, East, and West, they provide more precise guidance by using angle measurements.

Deciphering Directional Notation

Directional notation is a system used to describe a precise direction on the compass. When you hear 'E 70 S', it might sound cryptic at first, but it actually conveys a clear path.

Here's how to interpret it:

• The first letter, 'E', indicates our reference direction. In this case, we're standing somewhere east.
• The next part, '70', tells us how many degrees off we need to move from the reference direction, heading towards the second letter.
• The final 'S' is our destination relative to the given point, meaning we're moving 70 degrees towards the south.

This notion is based on moving clockwise along the compass, making it intuitive once the system is understood. Such notation allows for accurate navigation without needing the complete circle of degrees.

Exploring Angle Measurement

Angle measurement is central to both directional notation and bearings. Angles are usually measured in degrees, with a full circle comprising 360 degrees. This complete circle represents all possible directions one could travel.

In navigation, the circle begins at North (0 degrees) and moves clockwise. For instance:

• East is at 90 degrees
• South is at 180 degrees
• West at 270 degrees

The movement between these points is divided by more angles. By understanding how many degrees an angle diverts from one direction to another, one can determine a precise bearing. For example, moving 70 degrees from south towards the east gives us the bearing 'E 70 S'.

This is why compass directions, directional notation, and angle measurement all work hand-in-hand to provide effective navigation tools. They allow us to describe direction more accurately and help us understand statements like 'The bearing from O to B is E 70 S'. This facilitates clear communication, whether in navigation or problem solving.