$module$/top/Implicit pentru Test Teoreme in triunghiul dreptunghic+valori trigonometrice Categoria implicită pentru întrebările partajate în contextul 'Test Teoreme in triunghiul dreptunghic+valori trigonometrice'. 7_G_3_calculat_nivel2_02 Calculați lungimea înălțimii din unghiul drept.]]> Se aplica teorema înălțimii. 1.0000000 0.3333333 0 1 0 abc 1 sqrt({x}*{y}) 0.01 1 1 2 Bravo! 0 0.1000000 3 0 private x calculated uniform 1 10 0 100 1 2 2 7 3 5 4 10 5 4 6 4 7 8 8 3 9 2 10 4 11 2 12 10 13 9 14 8 15 1 16 3 17 2 18 7 19 7 20 7 21 3 22 4 23 3 24 9 25 10 26 3 27 9 28 6 29 3 30 1 31 8 32 1 33 9 34 3 35 6 36 1 37 7 38 2 39 5 40 6 41 4 42 8 43 9 44 2 45 4 46 8 47 10 48 7 49 10 50 2 51 9 52 7 53 6 54 2 55 8 56 5 57 4 58 9 59 6 60 2 61 9 62 1 63 4 64 4 65 6 66 2 67 6 68 5 69 9 70 8 71 10 72 4 73 4 74 10 75 3 76 4 77 5 78 5 79 6 80 6 81 7 82 6 83 2 84 1 85 8 86 2 87 8 88 4 89 8 90 3 91 9 92 1 93 9 94 4 95 6 96 2 97 3 98 6 99 4 100 1 100 private y calculated uniform 1 10 0 100 1 4 2 7 3 4 4 7 5 9 6 2 7 9 8 10 9 5 10 8 11 6 12 8 13 6 14 7 15 2 16 7 17 7 18 3 19 7 20 7 21 5 22 9 23 4 24 8 25 8 26 3 27 10 28 5 29 8 30 9 31 5 32 10 33 10 34 8 35 3 36 6 37 5 38 2 39 3 40 5 41 2 42 4 43 4 44 6 45 9 46 10 47 7 48 4 49 7 50 8 51 2 52 10 53 8 54 2 55 10 56 3 57 2 58 2 59 2 60 10 61 9 62 7 63 7 64 9 65 6 66 4 67 5 68 5 69 7 70 5 71 3 72 6 73 7 74 7 75 3 76 7 77 3 78 3 79 4 80 9 81 2 82 5 83 4 84 3 85 2 86 3 87 10 88 5 89 2 90 2 91 7 92 4 93 2 94 3 95 8 96 3 97 1 98 6 99 3 100 4 100 7_G_3_calculat_nivel2_03 Calculați lungimea catetei corespunzătoare.]]> Se aplica Teorema catetei. 1.0000000 0.3333333 0 1 0 abc 1 sqrt({h}*{l}) 0.01 1 1 2 0 0.1000000 3 0 private h calculated uniform 1 10 0 100 1 2 2 9 3 1 4 10 5 7 6 8 7 2 8 5 9 5 10 8 11 8 12 6 13 9 14 8 15 3 16 10 17 7 18 1 19 4 20 7 21 4 22 9 23 4 24 3 25 6 26 4 27 3 28 5 29 5 30 4 31 1 32 2 33 10 34 3 35 8 36 5 37 4 38 7 39 1 40 3 41 6 42 4 43 8 44 6 45 8 46 7 47 6 48 7 49 2 50 10 51 10 52 4 53 4 54 2 55 6 56 4 57 3 58 7 59 8 60 6 61 4 62 5 63 3 64 5 65 2 66 9 67 8 68 8 69 4 70 7 71 2 72 7 73 4 74 6 75 8 76 8 77 2 78 1 79 8 80 9 81 4 82 6 83 8 84 8 85 3 86 7 87 7 88 5 89 5 90 4 91 4 92 7 93 9 94 3 95 3 96 5 97 10 98 4 99 1 100 3 100 private l calculated uniform 1 10 0 100 1 6 2 1 3 2 4 2 5 2 6 7 7 6 8 6 9 3 10 10 11 3 12 9 13 10 14 6 15 3 16 7 17 8 18 3 19 8 20 3 21 2 22 8 23 3 24 7 25 4 26 3 27 2 28 3 29 4 30 4 31 6 32 6 33 8 34 8 35 8 36 6 37 9 38 8 39 5 40 6 41 5 42 3 43 2 44 4 45 6 46 9 47 7 48 1 49 5 50 6 51 10 52 1 53 7 54 2 55 1 56 8 57 4 58 9 59 4 60 7 61 4 62 4 63 3 64 4 65 3 66 2 67 6 68 4 69 4 70 2 71 5 72 6 73 10 74 4 75 9 76 10 77 1 78 5 79 5 80 8 81 2 82 10 83 2 84 4 85 5 86 3 87 4 88 2 89 4 90 6 91 4 92 8 93 3 94 3 95 7 96 4 97 9 98 4 99 5 100 3 100 7_G_3_calculat_nivel2_04 Calculați lungimea medianei dusă din unghiul drept.
]]> Se aplica teorema medianei în triunghiul dreptunghic: mediana corespunzatoare ipotenuzei = jumătate din ipotenuză. 1.0000000 0.3333333 0 1 0 abc 1 {l}/2 0.01 1 1 2 0 0.1000000 3 0 private l calculated uniform 1 10 1 100 1 8.5 2 9.2 3 6.8 4 7.2 5 1.7 6 1.7 7 2 8 6.2 9 1.6 10 2.6 11 9.3 12 6.5 13 4.4 14 3.8 15 8.7 16 5 17 5.6 18 2.5 19 1.6 20 5.6 21 9.9 22 3.4 23 2.1 24 5.3 25 1.7 26 7.4 27 6.6 28 8 29 8.5 30 7.8 31 7.4 32 8.3 33 1.4 34 1.5 35 2.2 36 7.8 37 5.9 38 6.6 39 6 40 6.8 41 4.7 42 9.3 43 6.6 44 3.8 45 3.5 46 8.5 47 3.3 48 7.5 49 2.6 50 8.1 51 7.7 52 5.3 53 1.7 54 9.1 55 5.9 56 9.3 57 1.2 58 7.9 59 7.6 60 4.1 61 7.7 62 1.4 63 2 64 5.1 65 5.4 66 2.4 67 8 68 3.6 69 1.3 70 6.9 71 9 72 3.6 73 3.2 74 9.6 75 5 76 2.6 77 2.5 78 7.4 79 2.7 80 1.8 81 1.1 82 8.4 83 1.6 84 9.4 85 4.8 86 6.6 87 2.7 88 1.7 89 4.8 90 3.6 91 4.9 92 9.1 93 1.9 94 7.7 95 9.7 96 9.6 97 9.1 98 6.1 99 8.7 100 9.9 100 7_G_3_calculat_nivel2_05 Calculați sin B.]]> Cum unghiul B este în colțul B, cateta opusă este AB. ⇒ sin B = AB / BC = {AB}/{BC} = {round({y}/{x}, 2)}.]]> 1.0000000 0.3333333 0 2 0 abc 1 {y}/{x} 0.05 1 1 2 0 0.1000000 3 0 private y calculated uniform 1 5 0 100 1 3.8 2 2.8 3 3.7 4 5 5 2.6 6 2.4 7 2.4 8 4.7 9 4.6 10 3.7 11 4 12 1.7 13 4.1 14 2.1 15 3 16 3 17 3.1 18 1.2 19 2 20 1.5 21 1.6 22 5 23 1.5 24 4.4 25 4.9 26 4 27 3.1 28 1 29 2.8 30 3 31 1.4 32 1.6 33 1.2 34 3.5 35 1 36 4.8 37 2.2 38 2.3 39 2.7 40 4.2 41 4.3 42 2.6 43 4.1 44 3.9 45 1.2 46 4.8 47 1.1 48 4.1 49 3.2 50 3.3 51 3.1 52 1.6 53 2.6 54 1.7 55 4.9 56 2.1 57 1.8 58 2.6 59 1.6 60 4.4 61 4.8 62 1.2 63 4.7 64 1.1 65 1.7 66 2.6 67 2 68 4.9 69 2 70 2.8 71 4.3 72 4.1 73 5 74 1.1 75 4.5 76 4.9 77 2.9 78 4.9 79 4.7 80 1.6 81 3.9 82 2 83 3.9 84 1 85 3.7 86 4.3 87 1.4 88 4.3 89 1.3 90 4.9 91 3.5 92 3.3 93 1.9 94 4.7 95 3.7 96 3.4 97 2.6 98 4.6 99 5 100 3.5 100 private x calculated uniform 6 10 0 100 1 6.2 2 9.2 3 8 4 7.5 5 9.1 6 6.3 7 8.1 8 9.5 9 7.3 10 9 11 9.7 12 8.6 13 9.7 14 9.6 15 6.5 16 9.7 17 7 18 7.9 19 6.3 20 9.2 21 6.1 22 10 23 8.7 24 6.6 25 7.9 26 8.4 27 8.3 28 9 29 9.8 30 9 31 6.9 32 6.2 33 8.3 34 7.5 35 9.7 36 8 37 6.2 38 8.4 39 6.9 40 9.8 41 8.4 42 8.5 43 7.3 44 7 45 9.6 46 7.9 47 9.2 48 8.7 49 6 50 8.4 51 8.7 52 7.3 53 8.9 54 7.4 55 9.8 56 8.1 57 7.3 58 6.9 59 9.9 60 8.5 61 6.5 62 8 63 8.7 64 9.1 65 9.4 66 8.4 67 8.4 68 9.2 69 6.6 70 8.5 71 6.5 72 6.1 73 9 74 8.3 75 8.9 76 7.2 77 6.5 78 8 79 7.8 80 6.6 81 8.6 82 7.1 83 7.5 84 8.1 85 6.6 86 9.9 87 9.1 88 9.2 89 8.6 90 6.8 91 7.5 92 8.4 93 8 94 9.3 95 6.2 96 9.5 97 8.6 98 8.6 99 9.9 100 8.1 100 7_G_3_calculat_nivel2_06 Calculați lungimea ipotenuzei BC.]]> Deci ipotenuza BC = AB / cos B = {AB}/{cosB} = {round({AB}/{cosB}, 2)} cm.]]> 1.0000000 0.3333333 0 1 0 abc 1 {AB}/{cosB} 0.01 1 1 2 0 0.1000000 3 0 private AB calculated uniform 5 10 1 100 1 7.9 2 5.2 3 6.7 4 7.7 5 5.6 6 9.3 7 9.3 8 5 9 6.4 10 9 11 9.8 12 7 13 7.6 14 9.4 15 9 16 10 17 5.6 18 7.8 19 6.1 20 9.2 21 7.1 22 8.2 23 7.7 24 5.6 25 9.6 26 7 27 6 28 6.9 29 7.7 30 9.3 31 9.7 32 5.9 33 6.5 34 6.3 35 6.2 36 5.7 37 5.5 38 9.3 39 7.9 40 6.2 41 9.4 42 6.1 43 5.1 44 6.9 45 6.4 46 8.2 47 8.4 48 6.2 49 8.9 50 6.1 51 7.9 52 6.2 53 7.8 54 6.7 55 6.5 56 5.9 57 5.8 58 5.6 59 9.3 60 8.9 61 7 62 8.1 63 5.4 64 7.8 65 7.8 66 9.4 67 8.4 68 7.3 69 5.6 70 6.5 71 8.1 72 7.3 73 9.4 74 6.1 75 6.5 76 8 77 7.4 78 8.4 79 6.1 80 5.4 81 6.6 82 5.2 83 8.5 84 7 85 7.3 86 7.8 87 9.6 88 6.6 89 9.9 90 6.3 91 6 92 8.2 93 6.3 94 9.1 95 9.3 96 6.5 97 6.9 98 7.2 99 9.7 100 5 100 private cosB calculated uniform 0.1 0.9 1 100 1 0.7 2 0.4 3 0.4 4 0.7 5 0.3 6 0.1 7 0.2 8 0.5 9 0.9 10 0.2 11 0.3 12 0.9 13 0.7 14 0.6 15 0.4 16 0.2 17 0.6 18 0.6 19 0.3 20 0.8 21 0.6 22 0.4 23 0.9 24 0.7 25 0.2 26 0.3 27 0.2 28 0.7 29 0.5 30 0.4 31 0.2 32 0.1 33 0.7 34 0.1 35 0.3 36 0.4 37 0.2 38 0.5 39 0.6 40 0.5 41 0.3 42 0.7 43 0.2 44 0.1 45 0.2 46 0.8 47 0.2 48 0.4 49 0.8 50 0.2 51 0.7 52 0.1 53 0.2 54 0.3 55 0.6 56 0.8 57 0.8 58 0.9 59 0.7 60 0.6 61 0.4 62 0.3 63 0.3 64 0.8 65 0.1 66 0.6 67 0.5 68 0.5 69 0.7 70 0.5 71 0.6 72 0.6 73 0.3 74 0.8 75 0.7 76 0.4 77 0.2 78 0.6 79 0.9 80 0.4 81 0.4 82 0.4 83 0.6 84 0.3 85 0.2 86 0.8 87 0.5 88 0.2 89 0.2 90 0.7 91 0.3 92 0.6 93 0.5 94 0.8 95 0.7 96 0.8 97 0.1 98 0.1 99 0.8 100 0.6 100 7_G_3_calculat_nivel2_07 Calculați lungimea catetei AC.]]> ⇒ AC = tg B × AB = {tgB} × {AB} = {round({tgB}*{AB}, 2)} cm.]]> 1.0000000 0.3333333 0 1 0 abc 1 {tgB}*{AB} 0.01 1 1 2 0 0.1000000 3 0 private tgB calculated uniform 0.1 2 1 100 1 0.9 2 1.2 3 1.3 4 1.6 5 0.5 6 0.2 7 1.2 8 0.9 9 1 10 0.8 11 1.5 12 1.4 13 0.3 14 0.3 15 0.8 16 0.8 17 1.3 18 1.6 19 1.9 20 0.1 21 2 22 1.6 23 1.2 24 0.9 25 1 26 1.9 27 0.3 28 0.1 29 0.2 30 1.4 31 1.5 32 1 33 1.6 34 1.4 35 0.2 36 0.5 37 0.4 38 0.7 39 1 40 1.7 41 0.1 42 2 43 1.2 44 0.1 45 0.8 46 1.2 47 0.7 48 0.4 49 1.9 50 0.8 51 0.3 52 1 53 0.4 54 1.6 55 1.9 56 0.2 57 0.3 58 0.8 59 1.2 60 0.7 61 0.6 62 1.8 63 0.9 64 0.2 65 0.8 66 2 67 0.5 68 0.3 69 0.7 70 0.8 71 1.4 72 1.2 73 1.4 74 0.9 75 1.3 76 0.6 77 1.6 78 1.4 79 0.9 80 0.6 81 1.1 82 1.3 83 0.8 84 0.4 85 0.9 86 1.2 87 1.1 88 1.4 89 0.6 90 1.3 91 1.3 92 1.8 93 0.3 94 1.8 95 1.5 96 1.6 97 2 98 1.3 99 0.9 100 1.3 100 private AB calculated uniform 4 6 1 100 1 4.5 2 4.2 3 4 4 4.9 5 5.2 6 5 7 4.5 8 4.3 9 4.9 10 4.2 11 4.7 12 5.5 13 5.1 14 5.2 15 5.5 16 4.3 17 4.8 18 6 19 5.1 20 4.2 21 4.5 22 5.6 23 6 24 4.1 25 5.7 26 4.6 27 5 28 4.2 29 5.6 30 4.2 31 4.2 32 4.9 33 5.6 34 4.3 35 5.2 36 5.2 37 4.9 38 4.8 39 5.1 40 4.2 41 5.6 42 4.8 43 4.1 44 4.6 45 4 46 5 47 4.2 48 4.3 49 5.8 50 4.8 51 5.2 52 4.5 53 5.5 54 5.2 55 4 56 5.6 57 5 58 5.4 59 4.8 60 5.8 61 5.3 62 4.7 63 4.3 64 4.5 65 5.1 66 4.2 67 5.1 68 6 69 4.1 70 5.8 71 4.8 72 5.5 73 5.5 74 4.9 75 4.5 76 4 77 4 78 4.4 79 4.3 80 4 81 4.6 82 5.2 83 5.5 84 5.8 85 4.9 86 5.8 87 5.9 88 5.1 89 4.2 90 4.3 91 5.4 92 5.6 93 5.7 94 5.8 95 4.1 96 5.9 97 5.7 98 5 99 4.3 100 4.7 100 7_G_3_calculat_nivel2_08 Calculați cotangenta unghiului B.]]> 1.0000000 0.3333333 0 0 0 abc 1 {AB}/{AC} 0.01 1 1 2 0 0.1000000 3 0 private AB calculated uniform 4 10 0 100 1 7 2 7 3 5 4 8 5 7 6 7 7 10 8 7 9 8 10 8 11 6 12 8 13 4 14 8 15 9 16 6 17 4 18 9 19 7 20 6 21 7 22 8 23 10 24 7 25 6 26 9 27 8 28 8 29 5 30 4 31 6 32 5 33 6 34 8 35 5 36 6 37 8 38 9 39 4 40 5 41 10 42 9 43 9 44 5 45 8 46 7 47 9 48 10 49 8 50 8 51 9 52 5 53 5 54 9 55 9 56 8 57 8 58 6 59 9 60 6 61 7 62 6 63 10 64 4 65 5 66 10 67 9 68 10 69 7 70 10 71 6 72 6 73 8 74 8 75 8 76 5 77 9 78 5 79 10 80 6 81 4 82 6 83 10 84 9 85 7 86 5 87 7 88 8 89 7 90 5 91 6 92 7 93 9 94 4 95 7 96 9 97 9 98 10 99 8 100 6 100 private AC calculated uniform 4 10 0 100 1 6 2 6 3 6 4 8 5 7 6 4 7 5 8 7 9 6 10 4 11 5 12 7 13 9 14 4 15 8 16 5 17 7 18 4 19 8 20 10 21 7 22 6 23 9 24 5 25 6 26 10 27 7 28 5 29 8 30 8 31 6 32 10 33 5 34 8 35 7 36 10 37 5 38 6 39 6 40 6 41 4 42 8 43 8 44 6 45 5 46 7 47 7 48 8 49 8 50 5 51 10 52 7 53 4 54 5 55 5 56 5 57 5 58 10 59 9 60 9 61 9 62 7 63 7 64 10 65 7 66 6 67 6 68 6 69 5 70 7 71 5 72 6 73 7 74 5 75 9 76 4 77 5 78 10 79 7 80 7 81 4 82 5 83 9 84 4 85 9 86 6 87 5 88 8 89 7 90 6 91 6 92 5 93 6 94 9 95 9 96 5 97 6 98 8 99 9 100 5 100 7_G_3_calculat_nivel2_09
Calculați aria triunghiului ABC. 0.5*{AB}*(3/4)*{AB}]]> ⇒ AC = 3/4 × AB
Aria triunghiului ABC este: A = 1/2 × AB × AC = 1/2 × AB × (3/4 × AB) = 3/8 × AB².]]> 1.0000000 0.3333333 0 1 0 abc 1 0.5*{AB}*(3/4)*{AB} 0.01 1 1 2 0 0.1000000 3 0 private AB calculated uniform 5 10 0 100 1 8 2 9 3 9 4 7 5 6 6 7 7 5 8 7 9 7 10 9 11 10 12 9 13 5 14 7 15 6 16 9 17 9 18 9 19 10 20 9 21 6 22 8 23 8 24 10 25 6 26 7 27 9 28 7 29 9 30 9 31 7 32 8 33 8 34 8 35 9 36 9 37 7 38 7 39 9 40 7 41 6 42 8 43 8 44 7 45 8 46 8 47 8 48 9 49 7 50 6 51 8 52 8 53 8 54 8 55 9 56 8 57 6 58 6 59 8 60 7 61 10 62 6 63 8 64 10 65 9 66 9 67 7 68 8 69 10 70 7 71 6 72 9 73 10 74 6 75 9 76 7 77 6 78 7 79 6 80 9 81 8 82 7 83 8 84 9 85 6 86 8 87 8 88 5 89 7 90 9 91 7 92 8 93 6 94 8 95 10 96 6 97 10 98 9 99 9 100 6 100