10 SCREEN 12
20 WINDOW (-10, 10)-(10, -10)
30 LINE (-5, 3.2)-(3, 3.2)
40 LINE (-5, 3.2)-(0, 6.5)
50 LINE (0, 6.5)-(3, 3.2)
60 LINE (0, 6.5)-(0, 3.2)
70 LOCATE 10, 26
80 PRINT "B"
90 LOCATE 10, 48
100 PRINT "C"
110 LOCATE 8, 28
120 PRINT "c"
130 LOCATE 8, 48
140 PRINT "b"
190 LOCATE 11, 38
200 PRINT "a"
210 LOCATE 7, 39
220 PRINT "A"
230 LOCATE 1, 1
240 PRINT "                Proof of Heron's Formula"
250 PRINT "Prove Area of triangle = "; CHR$(251); "s(s-a)(s-b)(s-c) where s=(a+b+c)/2"
260 PRINT "Formula may also be written: Area=("; CHR$(251); "(a+b+c)(a+b-c)(b+c-a)(c+a-b))/4"
270 LOCATE 12, 1
280 PRINT "By the law of cosines cos(C)=(a^2+b^2-c^2)/2ab"
290 PRINT "sin(C)="; CHR$(251); "(1-cos^2(C))=("; CHR$(251); "(4a^2b^2-(a^2+b^2-c^2)^2))/2ab"
300 PRINT "The altitude of the triangle on base a = bsin(C)"
310 PRINT "Area=(1/2)*base*altitude"
320 PRINT "=(1/2)absin(C)"
330 PRINT "=(1/4)"; CHR$(251); "(4a^2b^2-(a^2+b^2-c^2)^2)"
340 PRINT "=(1/4)"; CHR$(251); "((2ab-(a^2+b^2-c^2))(2ab+(a^2+b^2-c^2)))"
350 PRINT "=(1/4)"; CHR$(251); "((c^2-(a-b)^2)((a+b)^2-c^2))"
360 PRINT "=(1/4)"; CHR$(251); "(c-(a-b))((c+(a-b))((a+b)-c))((a+b)+c)"
370 PRINT "="; CHR$(251); "(s(s-a)(s-b)(s-c))"
380 PRINT "The difference of two squares factorization was used in two different steps."
390 SYSTEM