1)Sabc = 1/2AB•AC=8
2)Sabc = Sahc + Sahb = 1/2AC•AH•sin60° + 1/2AB•AH•sin30°
AH = x
Sabc = ✓3x + x
3)(✓3+1)x= 8
x = 8/✓3+1 = 4✓3 - 4
4)HC² = AH²+AC²-2AH•AC•cos60° =
(4✓3-4)² + 16 - 4(4✓3-4) = 38-32✓3+16+16-16✓3+16 = 86-48✓3 = 48(2-✓3)
HC = 4✓(3(2-✓3))
1)Sabc = 1/2AB•AC=8
2)Sabc = Sahc + Sahb = 1/2AC•AH•sin60° + 1/2AB•AH•sin30°
AH = x
Sabc = ✓3x + x
3)(✓3+1)x= 8
x = 8/✓3+1 = 4✓3 - 4
4)HC² = AH²+AC²-2AH•AC•cos60° =
(4✓3-4)² + 16 - 4(4✓3-4) = 38-32✓3+16+16-16✓3+16 = 86-48✓3 = 48(2-✓3)
HC = 4✓(3(2-✓3))