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Sprendimas:
Pagal kosinusų teoremą atstumas lygus
saknis(
1^2+ 1^2- 2* 1* 1* cos(120)) =
1^2+ 1^2- 2* 1* 1* cos(120)) = |
|
saknis( 1^2+ 1^2- 2* 1* 1* cos(120)) = $$\sqrt {1^{2}+1^{2}-2\cdot 1\cdot 1\cdot cos(120)}$$ =
1^2+ 1^2- 2* 1* 1* cos(120)) = $$\sqrt {1^{2}+1^{2}-2\cdot 1\cdot 1\cdot cos(120)}$$ = $${\normalsize 1^{2}+1^{2}}$$ = $${\normalsize 2}$$
saknis(2- 2* 1* 1* cos(120)) = $$\sqrt {2-2\cdot 1\cdot 1\cdot cos(120)}$$ =
2- 2* 1* 1* cos(120)) = $$\sqrt {2-2\cdot 1\cdot 1\cdot cos(120)}$$ = $${\normalsize 2\cdot 1\cdot 1\cdot cos(120)}$$ = $${\normalsize 2\cdot cos(120)}$$
saknis(2- 2* cos(120)) = $$\sqrt {2-2\cdot cos(120)}$$ =
2- 2* cos(120)) = $$\sqrt {2-2\cdot cos(120)}$$ = $${\normalsize cos(120)}$$ = $${\normalsize -\frac{1}{2}}$$
saknis(2+
) = $$\sqrt {2+\frac{2\cdot 1}{2}}$$ =
2+ | 2* 1 |
| / 2 |
$${\normalsize \frac{2\cdot 1}{2}}$$ = $${\normalsize 1}$$
saknis(2+1) = $$\sqrt {2+1}$$ =
2+1) = $$\sqrt {2+1}$$ = $${\normalsize 2+1}$$ = $${\normalsize 3}$$
saknis(3) = $$\sqrt {3}$$ =
3) = $$\sqrt {3}$$ = $${\normalsize \sqrt {3}}$$ = $${\normalsize 1.73}$$
1.73$$1.73$$
$$\sqrt {1^{2}+1^{2}-2\cdot 1\cdot 1\cdot cos(120)}$$ = $$$$
$$\sqrt {2-2\cdot cos(120)}$$ = $$$$
$$\sqrt {2+\frac{2\cdot 1}{2}}$$ = $$$$
$$\sqrt {2+1}$$ = $$$$
$$\sqrt {3}$$ = $$$$
$$1.73$$ $$$$
Atsakymas: 1.73 m