https://file.aiquickdraw.com/mathbot/file/1727112413732cty0mc0o.jpg

We are tasked with calculating the bearing of point \( C \) from point \( A \).

### Step-by-step approach:

1. **Identify the right triangle**: The diagram shows a right-angled triangle \( \triangle ABC \) with:
   - \( AB = 5 \, \text{km} \) (the horizontal distance)
   - \( BC = 8 \, \text{km} \) (the vertical distance).

2. **Bearing definition**: A bearing is measured clockwise from north. We need to find the angle \( \theta \), where \( \theta \) is the angle between line \( AC \) and the north direction from \( A \).

3. **Trigonometric relationship**:
   - The bearing angle \( \theta \) can be found using the tangent function, since we have the opposite side \( BC \) and the adjacent side \( AB \):
   \[
   \tan(\theta) = \frac{AB}{BC} = \frac{5}{8}.
   \]

4. **Calculate the angle**:
   \[
   \theta = \tan^{-1}\left(\frac{5}{8}\right).
   \]

Let me calculate this for you.The bearing of point \( C \) from point \( A \) is \( 58.0^\circ \), measured clockwise from north.

Would you like more details or have any questions?

Here are some related questions to expand on this concept:
1. How do bearings change when distances are reversed between points?
2. How can you use other trigonometric functions to find angles in similar problems?
3. What is the significance of the right triangle in navigation problems like this one?
4. How would the bearing change if point \( C \) was directly east of point \( A \)?
5. How can Pythagoras' Theorem be used to check the distances in this problem?

**Tip**: Bearings are always measured clockwise from the north, and a full bearing can range from \( 0^\circ \) to \( 360^\circ \).

Calculate the bearing of point C from point A. B is 5 km due east of turbine A, and C is 8 km due north of turbine B. Give your answer correct to 1 decimal place.

Learn how to calculate the bearing of point C from point A in a right-angled triangle, where AB is 5 km and BC is 8 km. This problem involves trigonometric concepts like tan(θ) and bearings, and is suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation