konum
3
|AB | sinθ 21 = | A 0 A | sin β β = sin −1 [ | A 0 A | | AB | . sin θ 21 ] β = f ( θ 21 ) | A 0 B | 2 = | A 0 A | 2 + |AB | 2 - 2. | A 0 A | .| AB |. cos α (1) |AB | 2 = | A 0 A | 2 + | A 0 B | 2 - 2. | A 0 A | . | A 0 B |. cos θ 21 (2) | A 0 A | 2 = |AB | 2 + | A 0 B | 2 - 2.| AB | . | A 0 B | . cos β (3) (2) denkleminden (3) denklemini çıkaralım. |AB | 2 - | A 0 A | 2 = | A 0 A | 2 + | A 0 B | 2 - 2. | A 0 A | . | A 0 B |. cos θ 21 - |AB | 2 - | A 0 B | 2 + 2.| AB | . | A 0 B | . cos β 2|AB | 2 - 2 | A 0 A | 2 = 2| A 0 B | . [ | AB |. cos β− | A 0 A | . cos θ 21 ] | A 0 B | = | AB | 2 − | A 0 A | 2 |AB |. cos β− | A 0 A | . cos θ 21 | A 0 B | =f ( θ 21 ) (1) denkleminden "α" çekilirse; α = cos -1 ( | A 0 A | 2 + | AB | 2 - | A 0 B | 2 2. | A 0 A | . |AB | ) α = f ( θ 21 ) x = | A 0 A | . sin θ 21 y = h - x sin γ = y |AD | , γ=¿ sin -1 y |AD | γ = f ( θ 21 )
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konum
Transcript of konum
|AB|sin θ21
= |A0 A|sin β
β = sin−1[|A0 A||AB|
. sin θ21] β = f (θ21)
|A0B|2 = |A0 A|2 + |AB|2 - 2.|A0 A|.|AB|. cosα (1)
|AB|2 = |A0 A|2 + |A0B|2 - 2.|A0 A|.|A0B|. cosθ21 (2)
|A0 A|2 = |AB|2 + |A0B|2 - 2.|AB|.|A0B|. cosβ (3)
(2) denkleminden (3) denklemini çıkaralım.
|AB|2 - |A0 A|2 = |A0 A|2 + |A0B|2 - 2.|A0 A|.|A0B|. cosθ21 - |AB|2 - |A0B|2 + 2.|AB|.|A0B|. cosβ
2|AB|2 - 2|A0 A|2 = 2|A0B|.[|AB|.cos β−|A0 A|.cos θ21 ]
|A0B|=|AB|2−|A0 A|
2
|AB|.cos β−|A0 A|.cos θ21
|A0B|=f (θ21)
(1) denkleminden "α" çekilirse;
α = cos-1 (|A0 A|2+ |AB|2
- |A0 B|2
2.|A0 A| . |AB| ) α = f (θ21)
x = |A0 A| . sinθ21
y = h - x
sin γ = y
|AD| , γ=¿ sin-1 y
|AD| γ = f (θ21)
θ21=2π=360 °
β = sin−1[|A0 A||AB|
. sin θ21] = sin−1[2055
. sin 360]β = 0°
|A0B|=|AB|2−|A0 A|
2
|AB|.cos β−|A0 A|.cos θ21
= 552−202
55 .cos0−20 .cos 0
|A0B|=75cm
α = cos−1 (|A0 A|2+ |AB|2
- |A0 B|2
2.|A0 A| . |AB| )=cos−1( 202+552−752
2.20 .55 )α = 180°
x = |A0 A| . sinθ21 = 20 . sin0
x = 0y = h - x → y = h = 43 cm
γ=¿ sin-1 y
|AD| = sin-1 4377
γ=34 °
