math bearing, determine the bearing on which a car drive from a park if it finish 30km east and 75km south

To determine the bearing of the car's direction, we need to calculate the angle between the north direction and the path it took from the park to its final location.

Given:
- The car finishes 30 km east and 75 km south of the park.

### Step 1: Calculate the angle relative to the east direction
We can use trigonometry, specifically the tangent function, which relates the opposite and adjacent sides of a right triangle. Here, the opposite side corresponds to the south direction (75 km) and the adjacent side corresponds to the east direction (30 km).

\[
\theta = \tan^{-1}\left(\frac{75}{30}\right)
\]

Let's calculate that angle.

\[
\theta = \tan^{-1}\left(2.5\right)
\]

\[
\theta \approx 68.2^\circ
\]

### Step 2: Convert the angle to a bearing
The angle \(\theta\) we calculated is measured clockwise from the east axis. To convert this to a bearing:
- Bearing is measured clockwise from the north.
- Since the car is driving southeast, we add \(90^\circ\) to this angle (since the angle \(\theta\) is measured from the east).

\[
\text{Bearing} = 90^\circ + 68.2^\circ = 158.2^\circ
\]

Thus, the car's bearing is approximately **158.2°**.

Would you like a deeper explanation, or do you have any other questions?

### Related questions:
1. What is the formula for calculating bearings in general?
2. How would the bearing change if the car traveled northwest instead?
3. How does the bearing differ from true north compared to magnetic north?
4. Can the bearing be negative, and if so, how is it interpreted?
5. How do you calculate distances between two points using bearings?

**Tip:** Bearings always start from the north (0°) and are measured clockwise!

Determine the bearing of a car traveling 30 km east and 75 km south using trigonometric functions and right triangle calculations. Learn how to use the tangent function and convert angles to bearings, suitable for high school students in Grades 9-12.

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