✔ 最佳答案
Notes :OA² = a² + b² + c²
OB² = b² + c²
OC² = a² + c²
OD² = a² + b²Soa / cos x
= a / { [a² + (a² + b² + c²) - ( b² + c²)] / [2a√(a² + b² + c²)] }
= √(a² + b² + c²)b / cos y
= b / { [c² + (a² + b² + c²) - (a² + b²)] / [2c√(a² + b² + c²)] }
= (b/c) √(a² + b² + c²)c / cos z
= c / { [b² + (a² + b² + c²) - (a² + c²)] / [2b√(a² + b² + c²)] }
= (c/b) √(a² + b² + c²)So√(a² + b² + c²) = (b/c) √(a² + b² + c²) = (c/b) √(a² + b² + c²)
1 = b/c = c/b
b = c
;cos x = a / √(a² + b² + c²) cos y = c / √(a² + b² + c²)cos z = b / √(a² + b² + c²)Set b = c = 1 , a = √2 :cos x = √2 / √(2+1+1) = √2 /2
x = 45°cos y = 1 / √(2+1+1) = 1/2
y = 60°
also
z = 60°Set b = c = 1 , a = 1 ,cos x = 1 / √3
x = 54.7°
also
y = 54.7°
z = 54.7°
Two set of (x , y , z) are (45° , 60° , 60°) and (54.7° , 54.7° , 54.7°)
