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Little explorations with HP calculators (no Prime)
04-10-2017, 04:49 PM
Post: #181
RE: Little explorations with the HP calculators
(04-10-2017 03:22 PM)telemachos Wrote:  To solve the two-triangles problem (pier4r's Post 122, above), I assumed that ABC was equilateral and had side length 12 units. That made its area 36√3 square units and made (x, y, z) = (6, 4, 3) units.

The law of cosines yielded side lengths (d, e, f) = (3√7, 7, 2√7) units for DEF. With an HP 50g in Exact mode (–105 CF) and with Rigorous mode on (–119 CF), Heron's formula then gave 21√3/2 square units for the area of DEF.

Finally, I scaled the areas of ABC and DEF by the factor 24/36√3 = 2/3√3, making those areas 24 (as required) and 7 square units respectively.

I did all of that with pencil and paper as well, but I was glad to have learned something about Rigorous mode, and to have written the little UserRPL program embodying Heron's formula.

Congratulations!

Since we correctly assumed the shape didn't matter, it strikes me that we all have missed perhaps the most convenient shape of all:

[Image: IMG_3069_zpsovzn2ukt.png]

Best regards,

Gerson.
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RE: Little explorations with the HP calculators - Gerson W. Barbosa - 04-10-2017 04:49 PM



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