§ 4: 4.6

4.6. Розв’яжіть трикутник за трьома сторонами.

1) а = 5 см; b = 6 см; c = 8 см. а² = b² + c² – 2bc • cos α. cos α =

= b2+ c2-a2 2bc = 36+64-252•6•8 = 0,7812; α = 37°;

bsinβ = asinα; sin β = b• sinαa = 6•0,6025 = 3,6125 = 0,7224; γ = 180° –

– (α + β) = 180° – 37° – 44° = 99°;

2) а = 21 см; b = 17 см; c = 32 см. b² = а² + c² – 2ac cos β;

cos β = a2+ c2-b2 2ac = 212+ 322-172 2•21•37 = 441+1024-2891344 = 11761344 = 0,875; β = 29°;

sinβb = sinαa;

sin α = a• sinβb = 21• sin29°17 = 21•0,48517 = 0,599;

α = 37°; γ = 180° – (α + β) = 180° – (29° + 37°) = 114°.