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Little explorations with HP calculators (no Prime)
04-10-2017, 03:22 PM
Post: #180
RE: Little explorations with the HP calculators
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.
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RE: Little explorations with the HP calculators - telemachos - 04-10-2017 03:22 PM

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