1. $P = 12\ \text{cm},\ A = 4\sqrt{3} = 6{,}93\ \text{cm}^2,\ \alpha = \beta = \gamma = 60^\circ,\ \alpha’ = \beta’ = \gamma’ = 120^\circ$
2. $\alpha = \beta = 43^\circ30′,\ \gamma = 93^\circ$
3. $6\ \text{cm}$
4. $45^\circ$
5. $a = 3\ \text{dm},\ b = 4\ \text{dm},\ \alpha = 36^\circ52′,\ \beta = 53^\circ08’$
6. $b = 2\sqrt{34} = 11{,}66\ \text{cm},\ m_b = \sqrt{106} = 10{,}3\ \text{cm}$
7a. $h = 8{,}31\ \text{m}$
7b. $\alpha = 77^\circ46’$
8. $|MN| = 2(6 + \sqrt{6}) = 16{,}9\ \text{cm}$
9. $a = b = 16\ \text{cm},\ c = 28\ \text{cm}$
10. $\angle ACD = 27^\circ$
11. $\alpha = 108^\circ,\ \beta = 54^\circ,\ \gamma = 18^\circ$
12. $a = 15\ \text{cm},\ b = 22\ \text{cm},\ c = 17\ \text{cm},\ \alpha = 42^\circ54′,\ \beta = 86^\circ38′,\ \gamma = 50^\circ29’$
13. $\alpha = 45^\circ,\ \beta = 60^\circ,\ \gamma = 75^\circ,\ b = \sqrt{3} = 1{,}73,\ c = 1{,}93$
14. $h = 325{,}7\ \text{m}$
15. $w = 14{,}6\ \text{m}$
16. $\gamma = 61^\circ03′,\ a = 30{,}28,\ b = 35{,}87,\ c = 33{,}94$
17. $P = 3 + \sqrt{3} = 4{,}73,\ A = \frac{\sqrt{3}}{2} = 0{,}87$
18. $a = 18{,}41\ \text{cm},\ b = 14{,}86\ \text{cm},\ c = 6{,}51\ \text{cm}$
19. $b = 15{,}24,\ c = 10{,}66,\ \alpha = 32^\circ04′,\ \gamma = 42^\circ21’$
20. $A = 3{,}85$
21. Da, $\gamma = 91^\circ18′ > 90^\circ$
22. $a = 20{,}86,\ b = 55{,}31,\ c = 68{,}06,\ \gamma = 119^\circ32’$
23. $105{,}16\ \text{N}$
24. $d_1 = 12{,}54\ \text{cm},\ d_2 = 7{,}14\ \text{cm}$
25. $a = 12\cdot\sqrt{\frac{7}{5}} = 14{,}2,\ b = 6\cdot\sqrt{\frac{13}{5}} = 9{,}67,\ c = 6\cdot\sqrt{\frac{41}{5}} = 17{,}18$
26. Trikotnik je pravokoten.
27. $r = 3$
28. $r = 17\ \text{cm}$
29. $a = 13,\ h = \frac{120}{13} = 9{,}23,\ e = 10,\ f = 24$
30. $b = \frac{15}{4} = 3{,}75,\ c = \frac{25}{4} = 6{,}25$
Geometrija v ravnini: vaje z rešitvami
Če iščete učitelja, ki vam lahko pomaga osvojiti, kako se izračuna ploščina trikotnika in kaj je Pitagorov izrek, hitro poiščite “inštruktor matematike Maribor” ali “inštrukcije matematike Velenje”. Na meet’n’learn ali v Facebook skupini se lahko v trenutku povežete z najboljšim zasebnim učiteljem.