Geometry Challenge

[Albert Chan]

(01-09-2024 06:18 AM)Johnh Wrote:  i reckon the angle BAD is 85 degrees exactly.
https://www.hpmuseum.org/forum/attachment.php?aid=13154

You are so close to getting exact solution! (below, angles in degree)

Code:

          (1 + cos10 - cos70) = (1 + sin40)
    _____A__________E
    70  / ＼ θ    90|
       /    ＼      |
      /       ＼    | (sin70 - sin10) = cos40 = sin50
     /          ＼  |
    /             ＼|
   / 70             D
B  -------- C

AD^2 = (1+sin40)^2 + cos40^2 = 1 + 2*sin40 + 1 = 4*(1+cos50)/2 = (2*cos25)^2
AD = 2*cos25

sinθ = DE / DA = (2*sin25*cos25) / (2*cos25) = sin25      → θ = 25
∠BAD = 180 - 70 - 25 = 85