Answered

IDNLearn.com: Where curiosity meets clarity and questions find their answers. Ask any question and receive comprehensive, well-informed responses from our dedicated team of experts.

Alex is facing East. He turns 45 degrees left, then 90 degrees right. He reverses direction. Next, Alex turns 45 degrees left, then reverses direction. Finally, he turns 270 degrees to the right.

In which direction is Alex now facing?

Sagot :

GinnyAnsweridn
Let's solve this step-by-step.

1. Initial Direction:
- Alex starts by facing East, which we will denote as 0 degrees.

2. First Turn:
- Alex turns 45 degrees to the left. Turning left means we subtract the angle from the current direction.
- Initial direction: 0 degrees (East)
- Calculating: [tex]\( 0 - 45 = -45 \)[/tex]
- To handle negative angles, we add 360 degrees (since a full circle is 360 degrees). Thus, [tex]\(-45 + 360 = 315\)[/tex].
- After this turn, Alex is facing 315 degrees, which corresponds to Northwest.

3. Second Turn:
- Alex then turns 90 degrees to the right. Turning right means we add the angle to the current direction.
- Current direction: 315 degrees
- Calculating: [tex]\( 315 + 90 = 405 \)[/tex]
- Since 360 degrees is a full circle, we take the remainder when divided by 360. So, [tex]\( 405 \mod 360 = 45 \)[/tex].
- After this turn, Alex is facing 45 degrees, which is Northeast.

4. First Reversal:
- Alex reverses direction, which means he turns 180 degrees from his current direction.
- Current direction: 45 degrees
- Calculating: [tex]\( 45 + 180 = 225 \)[/tex]
- After reversing, Alex is facing 225 degrees, which points Southwest.

5. Third Turn:
- Alex turns 45 degrees to the left.
- Current direction: 225 degrees
- Calculating: [tex]\( 225 - 45 = 180 \)[/tex]
- No adjustment needed since 180 degrees is within a full circle.
- After this turn, Alex is facing 180 degrees, which is South.

6. Second Reversal:
- Alex then reverses direction again.
- Current direction: 180 degrees
- Calculating: [tex]\( 180 + 180 = 360 \)[/tex]
- Since 360 degrees means a full circle, 360 degrees is equivalent to 0 degrees.
- After reversing, Alex is back to facing 0 degrees, which is East.

7. Final Turn:
- Finally, Alex turns 270 degrees to the right.
- Current direction: 0 degrees (East)
- Calculating: [tex]\( 0 + 270 = 270 \)[/tex]
- After this turn, Alex is facing 270 degrees, which is West.

Thus, after all these turns, Alex ends up facing West.
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.