Вправи 801 - 934 » 832

832. Користуючись малюнком 15.11, знайдіть синус, косинус і тангенс кутів α і β. √(9^2+ 12^2 ) = 15. sin α = 15/5 = 3; cos α = 9/15 = 3/5; tg α = 12/9, sin β = 9/15 = 3/5; cos β = 12/15 = 4/5; tg β = 9/12 = 3/4; sin α = 6/10, cos α = 8/10, tg α = 6/8, sin β = 8/10, cos β = 6/10, tg β = 8/6. CM = √(2 •8) = 4; sin α = 2/(2√5) = 1/√5, cos α = 4/(2√5) = 2/√5, tg α = 2/4 = 1/2, sin β = 8/(4√5) = 2/√5, cos β = 4/(4√5) = 1/√5, tg β = 8/4 = 2. AB = √(15^2+ 8^2 ) = √(225+64) = 17; ∠ACK = 90° – β = α; ∠CBA = 90° – β, отже ∠CBA = α; sin α = 8/17; cos α = 15/17; tg α = 8/15; sin β = 15/17; cos β = 8/17; tg β = 15/8.