How do I find the point on a line where the angle between two other points is the largest?

Gustav Källander shared this question 3 years ago

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I have a line f(x) = sin(22*)x - 3sin(22*) that forms and angle between the two points A (0,3) and B (0,11). How do I find where point C (f) creates the largest angle ACB?

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Michael Borcherds ● 3 years ago

Please post your .ggb file

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Gustav Källander ● 3 years ago

Ok! This includes some equations at theend which I hope will lead me to the solution, but it hasn't quite worked.

Files: Geogebra-angle....

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mire2 ● 3 years ago

Hi Gustav,

work with this - https://en.wikipedia.org/wiki/Law_of_cosines

The cosine is strictly monotically increasing between 0° and 180°, so you are looking for a minimum of the cosine.

See the attached file.

Greetings

mire2

Files: Angle_Extreme.g...

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Gustav Källander ● 3 years ago

I figured it out by creating a separate expression for the angle, whose largest value was the largest value for the angle.

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