Use the figure shown to solve Exercises 13–16.Find the bearing from O to A.

Verified step by step guidance

1. Identify the direction from point O to point A on the diagram.
2. Note that bearings are measured clockwise from the north direction.
3. Determine the angle between the north direction and the line OA.
4. Since the angle from north to east is 90 degrees, add the given angle from east to OA.
5. Calculate the total bearing by adding the angles from north to east and from east to OA.

Key Concepts

Bearings

Bearings are a way of describing direction using angles measured clockwise from the north. They are typically expressed in degrees, ranging from 0° to 360°. For example, a bearing of 90° indicates a direction due east, while a bearing of 270° indicates due west. Understanding how to read and interpret bearings is essential for navigation and solving problems related to angles and directions.

Angle Measurement

In trigonometry, angles can be measured in degrees or radians. The figure shows various angles formed at point O, which are crucial for determining the bearing from O to point A. To find the bearing, one must accurately calculate the angle based on the given angles in the diagram, ensuring that the measurements are taken in a clockwise direction from the north.

Trigonometric Relationships

Trigonometric relationships, such as sine, cosine, and tangent, are fundamental in solving problems involving angles and distances. In the context of bearings, these relationships can help determine the position of point A relative to point O by using the known angles. Understanding how to apply these relationships is key to solving navigation problems and finding bearings accurately.