An imperial tie-fighter spaceship is 25 parsecs south of a rebel x-wing ship. If the tie-fighter heads N72°W for 7.72 parsecs, what bearing should the x-wing use to intercept the imperial ship at a 90° angle?
An imperial tie-fighter spaceship is 25 parsecs south of a rebel x-wing ship. If the tie-fighter heads N72°W for 7.72 parsecs, what bearing should the x-wing use to intercept the imperial ship at a 90° angle?
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![**Problem:**
An imperial tie-fighter spaceship is 25 parsecs south of a rebel x-wing ship. If the tie-fighter heads \( \text{N72}^\circ\text{W} \) for 7.72 parsecs, what bearing should the x-wing use to intercept the imperial ship at a \( 90^\circ \) angle?
**Solution:**
*Consider using trigonometry to solve this problem. First, create a diagram of the situation:*
1. **Initial Position**: Place the x-wing at the origin of a coordinate system and the tie-fighter 25 parsecs south of it on the y-axis.
2. **Movement of Tie-Fighter**:
- From its position, the tie-fighter moves 7.72 parsecs in the direction \( \text{N72}^\circ\text{W} \).
- Decompose this movement into northern and western components using trigonometric functions:
- Northward component: \( 7.72 \cdot \cos(72^\circ) \)
- Westward component: \( 7.72 \cdot \sin(72^\circ) \)
3. **New Position of Tie-Fighter**:
- Calculate the new coordinates for the tie-fighter after its move.
4. **Intercept Path**:
- Determine the bearing that the x-wing must take to meet the tie-fighter at a \( 90^\circ \) angle to the path the tie-fighter took.
\( \angle \) and \( [\text{box below for answer}] \):
- Calculate the required angle using appropriate geometric methods
- Enter the final answer in the given box.
*Note: The solution involves understanding bearings and using trigonometric principles to calculate path angles and distances.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ed323b9-8e35-4824-8e78-fcaf55c6ad57%2F33637ade-7e36-46a4-8018-bc5bc69af2f3%2Fsw5t5gj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
An imperial tie-fighter spaceship is 25 parsecs south of a rebel x-wing ship. If the tie-fighter heads \( \text{N72}^\circ\text{W} \) for 7.72 parsecs, what bearing should the x-wing use to intercept the imperial ship at a \( 90^\circ \) angle?
**Solution:**
*Consider using trigonometry to solve this problem. First, create a diagram of the situation:*
1. **Initial Position**: Place the x-wing at the origin of a coordinate system and the tie-fighter 25 parsecs south of it on the y-axis.
2. **Movement of Tie-Fighter**:
- From its position, the tie-fighter moves 7.72 parsecs in the direction \( \text{N72}^\circ\text{W} \).
- Decompose this movement into northern and western components using trigonometric functions:
- Northward component: \( 7.72 \cdot \cos(72^\circ) \)
- Westward component: \( 7.72 \cdot \sin(72^\circ) \)
3. **New Position of Tie-Fighter**:
- Calculate the new coordinates for the tie-fighter after its move.
4. **Intercept Path**:
- Determine the bearing that the x-wing must take to meet the tie-fighter at a \( 90^\circ \) angle to the path the tie-fighter took.
\( \angle \) and \( [\text{box below for answer}] \):
- Calculate the required angle using appropriate geometric methods
- Enter the final answer in the given box.
*Note: The solution involves understanding bearings and using trigonometric principles to calculate path angles and distances.*
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