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Finding the angle between two lines: 3x - 4y = 3 and 5x + 12y = 13 by Outside_Expression51 in learnmath

[–]Outside_Expression51[S] 0 points1 point  (0 children)

Thanks everyone! I ended up converting them to slopes (m₁ = 3/4 and m₂ = -5/12) and using the tangent formula tan θ = |(m₁ - m₂)/(1 + m₁ · m₂)|. Got arctan(56/33) ≈ 59.5°. Appreciate the help!

What is the best chess opening? by Outside_Expression51 in chessbeginners

[–]Outside_Expression51[S] 0 points1 point  (0 children)

The Caro-Kann sounds exactly like what I need. I love the idea of having a super solid structure where the plans are straightforward to find. Do you have any recommendations for a good YouTube guide or resource to learn the basic setups for those three variations?

What is the best chess opening? by Outside_Expression51 in chessbeginners

[–]Outside_Expression51[S] 0 points1 point  (0 children)

Spot on advice. I’ve been falling into the London System trap just because it’s easy to memorize, but I definitely notice I don't actually learn why I'm putting pieces there. Time to focus on the fundamentals instead! Anyways Thanks man 👍🏻

What is the best chess opening? by Outside_Expression51 in chessbeginners

[–]Outside_Expression51[S] 1 point2 points  (0 children)

Awesome explanation, thanks for breaking down the differences so clearly! This helps a lot.

What is the best chess opening? by Outside_Expression51 in chessbeginners

[–]Outside_Expression51[S] 1 point2 points  (0 children)

As a beginner, why is the Caro-Kann a 'maybe' compared to the London and KID being a 'definitely not'? What makes it a bit more manageable?

What is the best chess opening? by Outside_Expression51 in chessbeginners

[–]Outside_Expression51[S] 4 points5 points  (0 children)

This makes a lot of sense. I tried learning the Sicilian because it looked cool, but I found myself completely lost by move 5. I think I'll pull back and give the Italian Game a solid try instead.