1) α = 53° 8'; β = 90° - α = 90° - 53° 8' = 36° 52'
b = 18; по теореме синусов
a/sin α = b/sin β
a = b * sin α / sin β = 18 * sin (53° 8') / sin (36° 52')
c = √(a^2 + b^2)
2) c = 65; β = 30° 30'; α = 90° - β = 59° 30'
a = c*sin α = 65*sin (30° 30')
b = c*sin β = 65*sin (59° 30')
3) a = 36; b = 15
c = √(36^2 + 15^2) = √(1296 + 225) = √(1521) = 39
sin α = a/c = 36/39 = 12/13
sin β = b/c = 15/39 = 5/13
4) a = 35; α = 22° 37'; β = 90° - α = 90° - 22° 37' = 67° 23'
По теореме синусов
a/sin α = b/sin β
b = a * sin β / sin α = 35 * sin (67° 23') / sin (22° 37')
c = √(a^2 + b^2)
Все синусы смотри в таблицах Брадиса или в калькуляторе считай.