Geometry Challenge

[Albert Chan]

Trig (numerical) solution

Solve by Casio FX-3650P Triangle Solver (can handle both SSS, SAS)
Note: this calculator implied multiply has higher precedence than ×/÷

P3 Wrote:?→A: ?→B: ?→C: B-C→Y:
-A≥0 ⇒ √(4BC(sin A⅃2)²+Y²→A◢
(A+Y)(A-Y)÷4→Y: √(Y(BC-Y→D◢
Y/BC: 2 sin^-1√Ans→X◢
A-C: (B+Ans)(B-Ans)/4AC: 2 sin^-1√Ans→Y◢
π^r-Y-X

Program is most accurate if side A is the smallest.
see https://www.hpmuseum.org/forum/thread-11...#pid107487

ΔBAD (sides AD,AB,BD = Program sides A,B,C), degree mode

[Prog] 3
A? -65 EXE     // negative side means angle between B,C
B? 1 EXE
C? 2 sin(170/2
EXE --> A = 1.812615574
EXE --> D = 0.902859012 (area)
EXE --> X = 64.99999999 (∠A)
EXE --> Y = 30 (∠B)
EXE --> 85.00000001 (∠C)