SOS segits

1)
`{:(a, b, c, alpha, beta, gamma),
(9 cm, 8 cm, color(red)9.785147 cm, color(red)59.802069^circ, color(red)50.197931^circ, 70^circ):}`

`c = sqrt(a^2 + b^2 - 2 * a * b * cos gamma) = sqrt(9^2 + 8^2 - 2 * 9 * 8 * cos 70) = sqrt(81 + 64 - 144 * 0.342020) = sqrt(145 - 49.250900) = sqrt(95.749099) = color(red)9.785147`

`alpha = "arc cos" (b^2 + c^2 - a^2) / (2 * b * c) = "arc cos" (8^2 + 9.785147^2 - 9^2) / (2 * 8 * 9.785147) = "arc cos" (64 + 95.749099 - 81) / 156.562350 = "arc cos" 78.749100 / 156.562350 = "arc cos" 0.502989 = color(red)59.802069`

`beta = 180 - alpha - gamma = 180 - 59.802069 - 70 = color(red)50.197931`



2)
Jelöljük az oldalakt betűkkel: `a = 18 cm`, `b = 32 cm`, `c = 40 cm`. A legkisebb szög `alpha`, amely a legkisebb oldallal szemben van, a legnagyobb szög `gamma`, amely a legnagyobb oldallal szemben van.

`alpha = "arc cos" (b^2 + c^2 - a^2) / (2 * b * c) = "arc cos" (32^2 + 40^2 - 18^2) / (2 * 32 * 40) = "arc cos" (1024 + 1600 - 324) / 2560 = "arc cos" 2300 / 2560 = "arc cos" 0.898438 = color(red)26.046562^circ`

`gamma = "arc cos" (a^2 + b^2 - c^2) / (2 * a * b) = "arc cos" (18^2 + 32^2 - 40^2) / (2 * 18 * 32) = "arc cos" (324 + 1024 - 1600) / 1152 = "arc cos" (-252) / 1152 = "arc cos" -0.218750 = color(red)102.635625^circ`