Right Triangle Simulation

Espressione 11: 0 less than or equal to "y" less than or equal to left parenthesis, StartFraction, StartRoot, 3 , EndRoot minus 1 Over 1 minus StartRoot, 3 , EndRoot , EndFraction , right parenthesis left parenthesis, "x" minus StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction "a" , right parenthesis plus StartFraction, "a" Over 2 , EndFraction left brace, StartFraction, "a" Over 2 , EndFraction less than "x" less than StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction "a" , right brace

Espressione 12: 0 less than or equal to "y" less than or equal to left parenthesis, StartFraction, 1 Over StartRoot, 3 , EndRoot minus 2 , EndFraction , right parenthesis left parenthesis, "x" minus "a" , right parenthesis left brace, StartFraction, StartRoot, 3 , EndRoot Over 2 , EndFraction "a" less than "x" less than "a" , right brace

Espressione 13: left parenthesis, "b" , 0 , right parenthesis

The next set of equations draws the linear line that forms the triangle in the first quadrant. I made the point (0,a) to be fixated at the endpoint of the quarter circle, so the triangular region depends on the point on the horizontal axis.

Espressione 15: "m" equals negative StartFraction, "a" Over "b" , EndFraction

Espressione 16: "y" equals "m" "x" plus "a"

Espressione 17: "b" equals 3.9 1

Espressione 18: 0 less than or equal to "y" less than or equal to "m" "x" plus "a" left brace, 0 less than "x" less than "a" , right brace

Make sure that when adjusting the value of b, the value of a is greater than the value of b.

Remark: You will end up obtaining 2 congruent triangular regions if the triangle is 30-60-90 or 45-45-90. This can easily be proven mathematically.

Espressione 21:

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