Facing North, X turns 205° clockwise and then 160° anticlockwise. In which direction X is facing now?
North-East
Understanding Directional Turns: Clockwise and Anticlockwise
This question involves understanding how turns in clockwise and anticlockwise directions affect your facing direction. We start facing a specific direction (North) and then apply a sequence of turns.
Initial State and Turns
- Initial Direction: Facing North.
- First Turn: 205° clockwise.
- Second Turn: 160° anticlockwise.
Calculating the Final Direction
We can solve this by considering the angles of the directions. North is typically considered 0° or 360°.
- Clockwise turns increase the angle from North (measured clockwise).
- Anticlockwise turns decrease the angle from North (measured clockwise), or increase the angle if measured anticlockwise. An anticlockwise turn from a position can be thought of as subtracting the angle from the current clockwise angle.
Step 1: First Turn (205° Clockwise from North)
Starting from North (0°), a 205° clockwise turn means the new direction is at an angle of 205° clockwise from North.
Current angle: $0° + 205° = 205°$.
Step 2: Second Turn (160° Anticlockwise)
From the current position (205° clockwise from North), X turns 160° anticlockwise. An anticlockwise turn subtracts from the clockwise angle.
New angle: $205° - 160° = 45°$.
Step 3: Determining the Final Direction
The final direction is at an angle of 45° clockwise from North.
Let's look at the standard angles for the main directions:
| Direction | Angle (Clockwise from North) |
|---|---|
| North | 0° / 360° |
| East | 90° |
| South | 180° |
| West | 270° |
| North-East | 45° |
| South-East | 135° |
| South-West | 225° |
| North-West | 315° |
An angle of 45° clockwise from North corresponds to the North-East direction.
Summary of Turns
- Start: North (0°)
- Turn 1: +205° (Clockwise) → 205°
- Turn 2: -160° (Anticlockwise) → $205° - 160° = 45°$
- Final Angle: 45° clockwise from North.
- Final Direction: North-East.
Therefore, after turning 205° clockwise and then 160° anticlockwise from North, X is facing North-East.
Revision Table: Direction and Angles
| Initial Direction | Clockwise Turn | Anticlockwise Turn | Net Change | Final Angle (from North) | Final Direction |
|---|---|---|---|---|---|
| North (0°) | +205° | -160° | $205° - 160° = 45°$ (Clockwise) | 45° | North-East |
Additional Information: Understanding Degrees in Directions
Thinking about directions in terms of degrees can make these types of problems easier. A full circle is 360°. The four main directions (North, East, South, West) are 90° apart.
- North is 0° (or 360°).
- East is 90° clockwise from North.
- South is 180° clockwise from North.
- West is 270° clockwise from North.
The intermediate directions (North-East, South-East, South-West, North-West) are exactly halfway between the main directions, meaning they are 45° from the nearest main direction.
- North-East is 45° clockwise from North.
- South-East is 45° clockwise from East (or 135° from North).
- South-West is 45° clockwise from South (or 225° from North).
- North-West is 45° clockwise from West (or 315° from North).
By converting turns into additions (clockwise) and subtractions (anticlockwise) of angles, you can easily find the final direction.
Similar Questions
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
