. .
:
a,b,c α, a, :
, .
:
ABC.
C AB CD.
, ADC , AD :
AD / AC = cos α
AD = AC cos α
AD = b cos α
BD AB AD:
BD = AB - AD
BD = c − b cosα
ADC BDC:
CD2 + BD2 = BC2
CD2 + AD2 = AC2
CD2 = BC2 - BD2
CD2 = AC2 - AD2
, :
BC2 - BD2 = AC2 - AD2
(a,b,c)
a2 - (c − b cos α)2 = b2 - (b cos α)2
a2 = (c − b cos α)2 + b2 - (b cos α)2
a2 = b2 + c 2 - 2bc cos α + (b cos α)2 - (b cos α)2
a2 = b2 + c 2 - 2bc cos α
, ( ), .
: .
8 , 120 . , 28 .
.
x, x+8 .
, :
282 = x2 + (x+8)2-2x(x+8)cos120o
784 = x2 + x2 +16x + 64 - 2x(x+8)(-0,5)
784 = 2x2+16x + 64 + x(x+8)
720 = 3x2 + 16x + 8x
3x2 + 24x +720 = 0
D=9216
x1=((-24)+96)/6=12 ( )
, P=12+(12+8)+28 = 60 .
: 60
7√3 , 1 . 150 . .
.
(.)
AB2 = (7√3)2 + 12 - 2 (7√3) cos 150º
150 .
AB2 = 147 + 1 - 14√3 (-√3/2)
AB2 = 148 + 21 = 169
AB = 13
: 13
́ , .
:
- - ;
- - ;
- - , .
, .
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, .
, , .
( ) , , , .
, . 180
, , :
- , ;
- ;
- , , .
, , , .
, .
, .
- n- (n − 2)π.
- n- 180(n − 2).
- n(n − 3) / 2, n .