.
45.
.
180 , , 180 - 90 = 90 .
BM AN - , 90 , (KAB KBA) 90 / 2 = 45 . , AKB AKB 180 - 45 = 135 .
, MKA 180 -135 = 45 . 45 .
, 45 135 .
.
. 4 6 . 10 . BE , , .. ?
.
.
, AEB DEC - .
AB2 + AE2 = BE2
CD2 + DE2 = CE2
, BE = CE,
AB2 + AE2 = CD2 + DE2
, AB = 4, CD = 6 ( , ),
AE2 + 42 = DE2 + 62
AE2 + 16 = DE2 + 36
, AE + DE = 10,
AE = 10 - DE
(10 - DE)2 + 16 = DE2 + 36
100 - 20DE + DE2 + 16 = DE2 + 36
80 = 20DE
DE = 4
AE = 10 - 4 = 6
,
AB2 + AE2 = BE2
42 + 62 = BE2
BE2 = 52
BE = 2√13
, 2√13
: BE = 2√13
.
ABC - . CD 6 . AD 2 . BD. ABC 180 . AC B.
.
BD = x, AD = x + 2
ABC ADC BDC. CD - , . , ABC :
CD * AD / 2 + CD * BD / 2 = 180
.
6 (x + 2) / 2 + 6x / 2 = 180
3 (x + 2) + 3x = 180
6x + 6 = 180
6x = 174
x = 29
, BD = 29, AD = BD + 2 = 29 + 2 = 31
AC BC.
BC2 = CD2 + BD2
AC2 = CD2 + AD2
BC2 = 292 + 62
AC2 = 312 + 62
AB = √877
AC = √997
: √877 √997
( 2)
. . .
S, α. , .
.
(S) :
S = 1/2 CD * AB
|
|
α.
AC = AB cos α
( cos α = AC /AB)
ADC. CD - , , CDA - .
CD = AC sin α
AC = AB cos α,
CD = AB cos α sin α
AB = CD / (cos α sin α)
.
S = 1/2 CD * AB
S = 1/2 CD * CD / (cos α sin α)
S = 1/2 CD2 / (cos α sin α)
, CD , .
CD2 = 2S cos α sin α
CD = √ (2S cos α sin α)