GEODEZJA

Ćwiczenie 4

Temat: Rachunek współrzędnych.

Radosław

Kwiatkowski

grupa 11B

2010/2011

1. Długość oraz azymut 12.

1. x₁=7,23 y₁=46,83

x₂=52,11 y₂=73,46

x₁₂=44,88

y₁₂=26,63

$d_{12} = \sqrt{{44,88}^{2} + {26,63}^{2}} = 52,19$

$\varphi = \operatorname{}{\frac{26,63}{44,88} = {34,0924}^{g}}$

A₁₂ = 34, 0924^g

1. x₁=28,73 y₁=31,12

x₂=7,04 y₂=45,21

x₁₂=-21,69

y₁₂=14,09

$d_{12} = \sqrt{{( - 21,69)}^{2} + {14,09}^{2}} = 25,86$

$\varphi = \operatorname{}{\frac{14,09}{- 21,69} = {- 36,6756}^{g}}$

A₁₂ = φ + 200 = 163, 3243^g

1. x₁=37,25 y₁=42,52

x₂=7,24 y₂=7,36

x₁₂=-30,01

y₁₂=-35,16

$d_{12} = \sqrt{{( - 30,01)}^{2} + {( - 35,16)}^{2}} = 46,23$

$\varphi = \operatorname{}{\frac{- 35,16}{- 30,01} = {55,0204}^{g}}$

A₁₂ = φ + 200 = 255, 0204^g

1. x₁=26,18 y₁=35,24

x₂=76,52 y₂=7,08

x₁₂=50,34

y₁₂=-28,16

$d_{12} = \sqrt{{50,34}^{2} + {( - 28,16)}^{2}} = 57,68$

$\varphi = \operatorname{}{\frac{- 28,16}{50,34} = {- 32,4694}^{g}}$

A₁₂ = φ + 400 = 367, 5306^g

1. Współrzędne pkt. 3

x₁=38,25 y₁=146,15

x₂=85,11 y₂=7,83

α = 39, 1275^g

d₁₃=34,75

x₁₂=46,86

y₁₂=-138,32

$\varphi = \operatorname{}{\frac{- 138,32}{46,86} = {- 79,2052}^{g}}$

A₁₂ = φ + 400 = 320, 7948^g

A₁₃ = A₁₂ − α = 281, 6673^g

x₃ = d₁₂ •  cosA₁₃ + x₁ = 28, 38

y₃ = d₁₂ •  sinA₁₃ + y₁ = 112, 83

1. Współrzędne pkt. 3

x₁=7,82 y₁=7,13

x₂=124,18 y₂=163,58

α = 25, 3374^g

β = 64, 5698^g

x₁₂=116,36

y₁₂=156,45

$\varphi = \operatorname{}{\frac{112,36}{152,45} = {59,2888}^{g}}$

A₁₂ = 59, 2888^g

A₁₃ = A₁₂ − α = 33, 9514^g

$d_{12} = \sqrt{{116,36}^{2} + {156,45}^{2}} = 194,98$

$d_{13} = \frac{d_{12} \bullet \sin\beta}{\sin{(\alpha + \beta)}} = \frac{194,98 \bullet \sin{64,5698}^{g}}{\sin{({25,3374}^{g} + {64,5698}^{g})}} = 167,65$

x₃¹ = x₁ + d₁₃ • cosA₁₃ = 7, 82 + 167, 65 • cos33, 9514^g = 152, 19

y₃¹ = y₁ + d₁₃ • sin=7, 13 + 167, 65 • sin=92, 36

A₂₁ = A₁₂ + 200 = 259, 2888^g

A₂₃ = A₂₁ + β = 323, 8586^g

$d_{23} = \frac{d_{12} \bullet \sin\alpha}{\sin{(\alpha + \beta)}} = \frac{194,98 \bullet \sin{25,3374}^{g}}{\sin{({25,3374}^{g} + {64,5698}^{g})}} = 76,53$

x₃² = x₂ + d₂₃ • cosA₂₃ = 124, 18 + 76, 53 • cos323, 8586^g = 152, 19

y₃² = y₂ + d₂₃ • sin=163, 58 + 76, 53 • sin=92, 36

$\mathbf{x}_{\mathbf{3}}\mathbf{=}\frac{\mathbf{x}_{\mathbf{3}}^{\mathbf{1}}\mathbf{+}\mathbf{x}_{\mathbf{3}}^{\mathbf{2}}}{\mathbf{2}}\mathbf{=}\mathbf{152,19}$

$\mathbf{y}_{\mathbf{3}}\mathbf{=}\frac{\mathbf{y}_{\mathbf{3}}^{\mathbf{1}}\mathbf{+}\mathbf{y}_{\mathbf{3}}^{\mathbf{2}}}{\mathbf{2}}\mathbf{=}\mathbf{92}\mathbf{,}\mathbf{36}$