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2010-03-14T09:03:50+01:00
Pacp = hx/2
Pabp = hy/2

4Pacp = Pabp => 4x = y
x = a/5
y = 4a/5
h = a√3/2

z tw. Pitagorasa:
|AP|² = |AD|² + |PD|²
|AP|² = h² + (y - a/2)²
|AP|² = h² + (3a/10)² = 3a²/4 + 9a²/100 = 84a²/100
|AP| = a2√21/10

z tw. sinusów:
x/sinα = |AP|/sin60° => sinα = x*sin60°/|AP|
y/sinβ = |AP|/sin60° => sinβ = y*sin60°/|AP|

sinα = x*sin60°/|AP| = (a/5) * (√3/2)/(a2√21/10) = √3/2√21 = 1/2√7 = √7/14
sinβ = y*sin60°/|AP| = (4a/5) * (√3/2)/(a2√21/10) = 4√3/2√21 = 2/√7 = 2√7/7

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