# Calculate the angle of an isosceles triangle to cover a distance on a plane

Knowing the points aand the angle alpha, calculate the necessary angle beta to cover a known distance C, on the Y plane.

The ab line segment is part of the triangle bisector.

• There doesn't seem to be enough information to solve this. Is the line from a to b is the bisector of the triangle? What do we know about the line from a to b?

• That's correct. A to B is the bisector of the triangle and we know its length since we know both points.

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Erdos
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• This was a very tricky problem! Let me know if you have any questions.

• Hi Erdos, thanks for your work. Excuse me for my lack of knowledge here, but shouldn't it be solved for the β beta angle? Also, I'm going to be using this in a game engine (Unity) where I can't seem to find a method for the squared tangent like it shows on your equation. Is it the same as tan(a) * tan(a) ?

• Erdos
+1

I added some more details at the end to show how you get beta. Yes, tan^2 (a)=tan (a) * tan (a).

• Erdos, at the end you say "multiplying by 2, you will get a formula for β", but I don't see that reflected in the formula. Can you please double-check?

• I just fixed it.

• Erdos, can you please tell me if there's a website where I can put this equation and then get a result by passing values to the variables (α, a1, b1 and c)? This would allow me to easily confirm if this returns correct values without having to implement it in the game engine.

• Erdos
+1

This can be done using a calculator: https://www.desmos.com/scientific

• Just implemented this and it works great, thank you very much!

• I am glad I was able to help.

• Erdos, I just realised that for very small numbers of α (between -1 an 1) I get slightly incorrect results. For 0 it returns NaN (not a number). Do you have any clue why this happens?

• Erdos
+1

I added some notes at the end of my solution.